Simplified Square Root Of 80

Foursquare root of lxxx = √80 = viii.94427191

Before evaluating the value of the square root of 80, allow'south recall the definition and representation of the square root. In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. Suppose a is the square root of b, it is represented every bit a = √b, or we tin express the same equation as a² = b. Here,'√' is the radical symbol used to denote the root of numbers. The positive number, when multiplied by itself, represents the square of the number. Thus, the foursquare root of the square of a positive number gives the original number.

In this commodity, you volition learn how to find the foursquare root of 80 in various methods with detailed explanations forth with representations and examples.

What is the Foursquare Root of 80?

The foursquare root of 80 is a number that, when multiplied by itself, gives the result as 80. The square root of lxxx is symbolically expressed as √lxxx.

Hence, √lxxx = √(Number × Number)

Let p exist the number.

(i.e) √80 = √(p × p)

√fourscore = √(p)2

So, p2 = 80

We can observe the possible value of p, which satisfies the in a higher place relation.

Let'south empathise how to find the square root of 80.

Square Root of eighty in Radical Form

To find the radical form of the foursquare root of 80, nosotros should use the prime number factorisation of 80. As we know, the prime factorisation of 80 is two × 2 × two × 2 × v. Permit united states of america write this as 16 × 5.

Here, 16 is a perfect square, whereas 5 is not. Thus, the foursquare root of eighty in radical form is expressed as follows:

√80 = √(two × two × two × 2 × v)

√80 = √(two)2.√(two)2 √3.

√80 = 2 × two ×√5

√80 = 4√5.

Therefore, the square root of lxxx in radical class is four√5.

Square Root of fourscore in Radical Form: 4√5.

Square Root of fourscore in Decimal Course

The decimal form of the foursquare root of 80 can be derived from the value of the radical form of the square root of 80.

As we already got the value of root 80 every bit four√5.

√fourscore = 4√5

Now, by substituting the value of the square root of 5 = 2.236, we get;

√fourscore = 4 × two.236 = 8.944

The square root of 80 in Decimal Form: viii.944

How to Summate the Square Root of 80

In mathematics, various methods are available to calculate the value of the square root of 80. They are:

Repeated subtraction method
Prime number factorisation method
Long partition method

All these methods are explained beneath with detailed explanations.

Square Root of 80 by Repeated Subtraction Method

In this method, we should subtract the successive odd numbers, i.e. i, 3, 5, seven,… till we obtain cypher, starting from fourscore and 1. The number of odd numbers nosotros decrease in this process is treated every bit the foursquare root of 80.

80 – ane = 79
79 – 3 = 76
76 – 5 = 71
71 – vii = 64
64 – 9 = 55
55 – 11 = 44
44 – 13 = 31
31 -fifteen = 16
sixteen – 17 = -1

A negative value cannot be possible; likewise, we didn't become 0 in the in a higher place subtraction but reached almost. Thus, from the higher up procedure, we can say that the square root of 80 value is between 8 and 9 besides as it is nearer to 9.

Click here to acquire more almost the square root of a number past the repeated subtraction method.

Square Root of lxxx by Prime Factorisation

In the prime factorisation method, nosotros have to separate the number by prime numbers starting from 2. When it cannot be divided further with 2, carve up information technology with the next prime number, i.e. 3 and continue this procedure till we get 1.

80 ÷ 2 = 40

At present, divide xl by 2.

forty ÷ two = twenty

Continue dividing by two.

20 ÷ 2 = 10

x ÷ 2 = 5

5 ÷ 2 = ii.5 (non a gene since the effect is not a whole number)

Try dividing five by other prime numbers such as 3.

five ÷ three = ane.6667 (non a factor since the result is not a whole number)

5 ÷ 5 = 1

Finally, we received the number 1 in the division procedure. So that we cannot go on further. Hence, the prime factorisation of 80 tin can be written as 2 x two × 2 ten 2 x 5 or ii⁶ × 5.

Prime factors can also be expressed equally given beneath:

Square root of 80 - Factors

Therefore, the prime factorisation of 80 is 2 × two × two × ii × 5.

Allow u.s. accept these factors as pairs.

That ways, 80 = (2 × two) × (two × 2) × (5)

Hither, we got two pairs of the aforementioned numbers, and 5 is left solitary.

Now, take the square root on both sides of the above representation.

√fourscore = √(ii × 2) × (2 × two) × (five) = 2 × 2 × √5 = 4√5.

Hence, the square root of eighty is equal to 4√five.

Square Root of 80 by Long Sectionalization Method

Go through the steps given below to learn how to observe the square root of fourscore by the long division method:

Step 1: Equally we know, eighty is not a perfect square; we need to put the decimal point and write pairs of 0s.

Step ii: Find the largest number whose square is less than or equal to the number in the leftmost group, i.e. eighty. We know that 8² < fourscore < 9², then we can consider 8. Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (fourscore). Past dividing the number, we get 16 as the remainder.

Step 3: Now, bring down 00 and add together the divisor with the quotient and enter information technology with a blank on its right. Now, we demand to identify the largest possible digit, which will also go the new digit in the caliber so that when the new divisor is multiplied by the new caliber, the production is less than or equal to the dividend. In this case, 169 × 9 = 1521, so nosotros choose the new digit as 9. Then, perform the division and get the balance.

Step four: Like to the previous footstep, bring down the side by side pair of 00 and follow the respective procedure. In this case, 1784 × 4 = 7136, so we choose the new digit as 4. Too, get the rest.

Step 5: Once again, bring down the next pair 00 and add the divisor with the quotient and enter it with a blank on its correct equally nosotros did in the previous steps. In this instance, 17884 × 4 = 71536, and then we choose the new digit equally 4. Finally, go the residue.

We tin can repeat this process as many times as required.

Square root of 80

Therefore, the caliber is equal to the square root of the number 80 upwards to 3 decimal places, i.e. √80 = 8.944.

Get Square Root of More Numbers Here

Video Lessons on Square Roots

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Solved Examples

Example 1:

Simplify: √5 × √80 – 16

Solution:

√v × √80 – xvi

= √5 × iv√5 – 16 {since in radical form √eighty = 4√5}

= 4(√five × √v) – 16

= (4 × 5) – 16

= 20 – 16

= four

Therefore, √5 × √eighty – 16 = 4.

Example ii:

Evaluate: x – √eighty + √5

Solution:

10 – √eighty + √five

= 10 – 4√five + √5

= 10 + √v(1 – 4)

= x – 3√five

Nosotros can simplify information technology farther by substituting the √5 value if required.

Frequently Asked Questions on Foursquare Root of 80

What is the value of the square root of eighty?

The value of the foursquare root of fourscore is eight.944271…

How do you detect the value of root 80?

We can find the square root of 80 in multiple ways, such equally repeated subtraction, prime factorisation and long partitioning method.

Square root of eighty is rational or irrational?

The square root of 80 is an irrational number every bit nosotros know that √80 = viii.944271.., non a rational number.

Is eighty a perfect foursquare?

No, 80 is non a perfect foursquare since the square root of eighty is not a whole number but a fraction value, i.east eight.8944…

What is the square of eighty?

The foursquare of 80 can exist written every bit 80^two, and it can be calculated as lxxx^two = eighty × 80 = 6400. Therefore, the square of fourscore is equal to 6400.