Square Root of 1521

In Mathematics, the square root of a number is a number, which when multiplied by itself results in the original number. Thus, the square root of 1521 is a number, which when multiplied by itself results in the number 1521. The square root of 1521 is a rational number as it can be expressed in the form of p/q. Here, we are going to discuss the value of the square root of 1521 and the methods such as prime factorization and the long division method to find the square root of 1521 are explained here in detail.

Table of Contents:

• What Is The Square Root Of 1521?
• Square Root Of 1521 In Radical Form
• Square Root Of 1521 By Prime Factorization Method
• Square Root Of 1521 By Long Division Method
• Solved Examples
• Practice Questions
• FAQs

What is the Square Root of 1521?

The square root of 1521 is a number, which when multiplied by itself and results in the number 1521. The square root of 1521 is symbolically expressed as √1521.

Hence, √1521 = √(Number × Number)

Thus, if we multiply the number 39 two times, we get the original value 1521.

(i.e) √1521 = √(39 × 39)

√1521 = √(39)²

Now, remove square and square root, we get

√1521 = ± 39

Square Root of 1521 in Radical Form

The simplest radical form of the square root of 1521 is √1521. The radical form of the square root of 1521 can be written if we know the prime factorization of 1521. We know that the prime factorization of 1521 is 3²×13². Hence, if we write the prime factorization of 1521 in the radical form, it will not be in the simplest form.

Square Root of 1521 by Prime Factorization Method

To find the square root of 1521 using the prime factorization method, one must know the prime factorization of 1521. We know that the prime factorization of 1521 is 3²×13².

Thus, √1521 = √[3×3×13×13]

√1521 = √[(3×3)×(13×13)]

This can also be written as

√1521 = √(3)². √(13)²

√1521 = 3×13 = 39.

Hence, the value of the square root of 1521 is 39.

Square Root of 1521 by Long Division Method

Follow the below steps to find the square root of 1521 using the long division method:

Step 1: Write the number 1521. Now, pair the number 1521 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 15 by a number, such that the product of the same number should be less than or equal to 15. Thus, 3×3 =9, which is less than 15. Thus, we obtained the quotient = 3 and remainder =6.

Step 3: Double the quotient value, so we get 6 and assume that 60 is the new divisor. Now, bring down the value 21 for division operation. So, the new dividend obtained is 621. Now, find the number, such that (60 + new number) × new number should give the product value, that should be less than or equal to 621. Hence, (60+9) × 9 = 621, which is equal to 621.

Step 4: Hence, the new quotient is 39 and the remainder is 0.

Step 5: Therefore, the value of the square root of 1521, √1521 is 39.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify √1521 + 10

Solution:

Given: √1521 + 10

We know that the value of the square root of 1521 is 39. Now, substitute the value in the above-given expression, we get

√1521 +10 = 39+10

√1521+10 = 49.

Hence, the simplified form of √1521 +10 is 49.

Example 2:

Find the value of m, if [78/(√1521)]+m = 10.

Solution:

Given: [78/(√1521)]+m = 10.

We know that √1521 = 39.

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

2+m = 10

m = 10-2 = 8

Hence, the value of m is 8.

Practice Questions

1. What is the value of 10 times square root of 1521?
2. Simplify (20√1521)+ 45.
3. Find the value of x, if 10x + √1521 = 60.

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