Square Root of 961

In Mathematics, the square root of 961 is a number, which when multiplied by itself results in the number 961. The square root of 961 is a rational number as it can be expressed in the form of p/q. In this article, we are going to learn the value of the square root of 961 and the methods such as prime factorization and the long division method to find the square root of 961 are explained with complete explanation.

What is the Square Root of 961?

The square root of 961 is a number, which when multiplied by itself and resulting in the number 961. The square root of 961 is symbolically expressed as √961.

Hence, √961 = √(Number × Number)

Thus, if we multiply the number 31 two times, we get the original value 961.

(i.e) √961 = √(31 × 31)

√961 = √(31)²

Now, remove square and square root, we get

√961 = ± 31

Square Root of 961 in Radical Form

The simplest radical form of the square root of 961 is √961. The radical form of the square root of 961 can be written if we know the prime factorization of 961. We know that the prime factorization of 961 is 31×31. Hence, if we write the prime factorization of 961 in the radical form, it will not be in the simplest form.

Square Root of 961 by Prime Factorization Method

To find the square root of 961 using the prime factorization method, one must know the prime factorization of 961. We know that the prime factorization of 961 is 31×31.

Thus, √961 = √[31×31]

√961 = √[(31×31)]

This can also be written as

√961 = √(31)²

On removing square and square root, we get

√961 = 31

Hence, the value of the square root of 961 is 31.

Square Root of 961 by Long Division Method

Follow the below steps to find the square root of 961 using the long division method:

Step 1: Write the number 961. Now, pair the number 961 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 9 by a number, such that the product of the same number should be less than or equal to 9. Thus, 3×3 =9, which is equal to 9. Thus, we obtained the quotient = 3 and remainder =0.

Step 3: Double the quotient value, so we get 6 and assume that 60 is the new divisor. Now, bring down the value 61 for division operation. So, the new dividend obtained is 61. Now, find the number, such that (60 + new number) × new number should give the product value, that should be less than or equal to 61. Hence, (60+1) × 1 = 61, which is equal to 61.

Step 4: Hence, the new quotient is 31 and the remainder is 0.

Step 5: Therefore, the value of the square root of 961, √961 is 31.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify √961 – 25

Solution:

Given: √961 – 25

We know that the value of the square root of 961 is 31. Now, substitute the value in the above-given expression, we get

√961 – 25 = 31 – 25

√961- 25 = 6

Hence, the simplified form of √961 – 25 is 6.

Example 2:

Find the value of x, if x + √961 = 40

Solution:

Given: x + √961 = 40.

We know that √961 = 31.

Now, substitute the value in the above equation, we get

x + 31 = 40

x = 40 – 31

x = 9

Hence, the value of x is 9.

Practice Questions

1. What is the value of 25 times square root of 961?
2. Simplify (15√961) – 100.
3. Find the value of a, if a – √961 = 91.

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