Square Root of 1024

In Mathematics, the square root of 1024 is a number, which when multiplied by itself results in the original number 1024. As the square root of 1024 is represented in the form of p/q, it is considered to be a rational number. Here, we are going to discuss the value of square root of 1024 using two different methods such as the prime factorization method and the long division method with complete explanation.

What is the Value of Square Root of 1024?

If a number is multiplied by itself and gives the result as 1024, then the number is the square root 1024. The square root of 1024 is symbolically expressed as √1024.

Hence, √1024 = √(Number × Number)

Thus, if we multiply the number 32 two times, we get the original value 1024.

(i.e) √1024 = √(32× 32)

√1024 = √(32)²

Now, remove square and square root, we get

√1024 = ± 32

Square Root of 1024 in Radical Form

The square root of 1024 can also be expressed in radical form. To express it in the simplest radical form, write the prime factorization of 1024. The prime factorization of 1024 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2. Thus, if we write the radical form (i.e) √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2), it should not be the simplest radical form. Therefore, the radical form of the square root of 1024 is √1024.

Square Root of 1024 by Prime Factorization Method

To find the square root of 1024 using the prime factorization method, we need to know the prime factorization of 1024. Thus, the prime factorization of 1024 is 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2.

Thus, √1024 = √(2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2)

√1024 = (√2)².(√2)².(√2)².(√2)².(√2)²

√1024 = 2×2×2×2×2

√1024 = 32

Hence, the square root of 1024 is equal to 32.

Square Root of 1024 by Long Division Method

The steps to find the square root of 1024 using the long division method is given as follows:

Step 1: Write the number 1024 in decimal form. Now, pair the number 1024 from right to left by putting the bar on the top of the number.

Step 2: Now, divide the number 10 by a number, such that the product of the same number should be less than or equal to 10. Thus, 3×3=9, which is less than 10. Thus, we obtained the quotient = 3 and remainder = 1.

Step 3: Double the quotient value, so we get 6 and assume that 60 is the new divisor. Now, bring down the value 24 for division operation. So, the new dividend obtained is 124. Now, find the number, such that (60 + new number) × new number should give the product value that should be less than or equal to 124. Hence, (60+2) × 2 = 124, which is equal to 124.

Step 4: Now subtract 124 from 124, and we get 00 as the new reminder, and 32 as a quotient.

Step 5: Thus, the value of the square root of 1024, √1024 is 32.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify 5√1024 +10.

Solution:

Given: 5√1024 +10

We know that the square root of 1024 is 32.

Now, substitute the value in the expression, we get:

5√1024 +10 = 5(32) + 10

5√1024 +10 = 160+10 = 170

Therefore, the simplified form of 5√1024 +10 is 170.

Example 2:

Find the value of m, if m√1024 – 4 = 92.

Solution:

Given: m√1024 – 4 = 92.

We know that √1024 = 32

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

m(32) – 4 = 92

32m = 92+4

32m = 96

m = 96/32

m = 3

Hence, the value of m is 3.

Example 3:

Simplify the expression: (4√1024 × 3√1024)

Solution:

Given expression: (4√1024 × 3√1024)

(4√1024 × 3√1024) = 12(√1024)²

On removing square and square root, we get

(4√1024 × 3√1024) = 12(1024) = 12288

Hence, the simplified form of (4√1024 × 3√1024) is 12288.