Square Root of 900

In Mathematics, the square root of a number is a number, which when multiplied by itself resulting in the original number. Thus, the square root of 900 is a number, which when multiplied by itself results in the number 900. The square root of 900 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 900 using different methods such as prime factorization and the long division method with complete explanation.

What is the Value of Square Root of 900?

The square root of 900 is a number, which when multiplied by itself and resulting in the number 900. The square root of 900 is symbolically expressed as √900.

Hence, √900 = √(Number × Number)

Thus, if we multiply the number 30 two times, we get the original value 900.

(i.e) √900 = √(30 × 30)

√900 = √(30)²

Now, remove square and square root, we get

√900 = ± 30

Square Root of 900 in Radical Form

The simplest radical form of the square root of 900 is √900. The radical form of the square root of 900 can be written if we know the prime factorization of 900. We know that the prime factorization of 900 is 2²×3²×5². Hence, if we write the prime factorization of 900 in the radical form, it will not be in the simplest form.

Square Root of 900 by Prime Factorization Method

To find the square root of 900 using the prime factorization method, one must know the prime factorization of 900. We know that the prime factorization of 900 is 2²×3²×5².

Thus, √900 = √[2×2×3×3×5×5]

√900 = √[(2×2)×(3×3)×(5×5)]

This can also be written as

√900 = √(2)².√(3)².√(5)²

√900 = 2×3×5 = 30.

Hence, the value of the square root of 900 is 30.

Square Root of 900 by Long Division Method

Follow the below steps to find the square root of 900 using the long division method:

Step 1: Write the number 900. Now, pair the number 900 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 00 for division operation. So, the new dividend obtained is 00. Now, find the number, such that (60 + new number) × new number should give the product value, that should be less than or equal to 0. Hence, (60+0) × 0 = 0, which is equal to 00.

Step 4: Hence, the new quotient is 30 and the remainder is 0.

Step 5: Therefore, the value of the square root of 900, √900 is 30.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify √900 + 90

Solution:

Given: √900 + 90

We know that the value of the square root of 900 is 30. Now, substitute the value in the above-given expression, we get

√900 + 90 = 30+90

√900+ 90 = 120.

Hence, the simplified form of √900 +90 is 120.

Example 2:

Find the value of x, if √900 – x = 10

Solution:

Given: √900 – x = 10.

We know that √900 = 30.

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

30 – x = 10

-x = 10-30

-x = – 20

x = 20

Hence, the value of x is 20.

Practice Questions

1. What is the value of 25 plus square root of 900?
2. Simplify [√900 + 30]/10
3. Find the value of x, if 30x + √900 = 60.

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