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Square Root of 976

The square root of 976 is expressed as √976 in the radical form and as (976)^½ or (976)^0.5 in the exponent form. The square root of 976 rounded up to 7 decimal places is 31.2409987. It is the positive solution of the equation x² = 976. We can express the square root of 976 in its lowest radical form as 4 √61.

Square Root of 976: 31.240998703626616
Square Root of 976 in exponential form: (976)^½ or (976)^0.5
Square Root of 976 in radical form: √976 or 4 √61

Square Root of 976

1.	What is the Square Root of 976?
2.	How to find the Square Root of 976?
3.	Is the Square Root of 976 Irrational?
4.	FAQs

What is the Square Root of 976?

The square root of 976, (or root 976), is the number which when multiplied by itself gives the product as 976. Therefore, the square root of 976 = √976 = 4 √61 = 31.240998703626616.

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How to Find Square Root of 976?

Square Root of 976 by Long Division Method

Value of √976 by Long Division Method

Explanation:

Forming pairs: 09 and 76
Find a number Y (3) such that whose square is <= 9. Now divide 09 by 3 with quotient as 3.
Bring down the next pair 76, to the right of the remainder 0. The new dividend is now 76.
Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 1) such that 6Z × Z <= 76. After finding Z, together 6 and Z (1) form a new divisor 61 for the new dividend 76.
Divide 76 by 61 with the quotient as 1, giving the remainder = 76 - 61 × 1 = 76 - 61 = 15.
Now, let's find the decimal places after the quotient 31.
Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
Add the last digit of quotient to divisor i.e. 1 + 61 = 62. To the right of 62, find a digit Z (which is 2) such that 62Z × Z <= 1500. Together they form a new divisor (622) for the new dividend (1500).
Divide 1500 by 622 with the quotient as 2, giving the remainder = 1500 - 622 × 2 = 1500 - 1244 = 256.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 976.

Therefore, the square root of 976 by long division method is 31.2 approximately.

Is Square Root of 976 Irrational?

The actual value of √976 is undetermined. The value of √976 up to 25 decimal places is 31.24099870362661757651889. Hence, the square root of 976 is an irrational number.

☛ Also Check:

Square Root of 16 - √16 = 4
Square Root of 98 - √98 = 9.89949
Square Root of 900 - √900 = 30
Square Root of 35 - √35 = 5.91608
Square Root of 116 - √116 = 10.77033
Square Root of 92 - √92 = 9.59166
Square Root of 136 - √136 = 11.66190

Square Root of 976 Solved Examples

Example 1: Solve the equation x² − 976 = 0

Solution:

x² - 976 = 0 i.e. x² = 976
x = ±√976
Since the value of the square root of 976 is 31.241,
⇒ x = +√976 or -√976 = 31.241 or -31.241.
Example 2: If the surface area of a cube is 5856 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 5856 in²
⇒ a = ±√976 in
Since length can't be negative,
⇒ a = √976
We know that the square root of 976 is 31.241.
⇒ a = 31.241 in
Example 3: If the area of a square is 976 in². Find the length of the side of the square.

Solution:

Let 'a' be the length of the side of the square.
⇒ Area of the square = a² = 976 in²
⇒ a = ±√976 in
Since length can't be negative,
⇒ a = √976 = 31.241 in

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FAQs on the Square Root of 976

What is the Value of the Square Root of 976?

The square root of 976 is 31.24099.

Why is the Square Root of 976 an Irrational Number?

Upon prime factorizing 976 i.e. 2⁴ × 61¹, 61 is in odd power. Therefore, the square root of 976 is irrational.

What is the Value of 3 square root 976?

The square root of 976 is 31.241. Therefore, 3 √976 = 3 × 31.241 = 93.723.

If the Square Root of 976 is 31.241. Find the Value of the Square Root of 9.76.

Let us represent √9.76 in p/q form i.e. √(976/100) = 9.76/10 = 3.124. Hence, the value of √9.76 = 3.124

Evaluate 5 plus 15 square root 976

The given expression is 5 + 15 √976. We know that the square root of 976 is 31.241. Therefore, 5 + 15 √976 = 5 + 15 × 31.241 = 5 + 468.615 = 473.615

What is the Square Root of 976 in Simplest Radical Form?

We need to express 976 as the product of its prime factors i.e. 976 = 2 × 2 × 2 × 2 × 61. Therefore, √976 = √2 × 2 × 2 × 2 × 61 = 4 √61. Thus, the square root of 976 in the lowest radical form is 4 √61.

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