Square Root of 1225

In Mathematics, the square root of 1225 is defined as a number, which on multiplication by itself for two times, results in the original number 1225. The value of the square root of 1225 is a rational number since it can be represented in the form of p/q. In this article, we will learn two different such as the long division method and the prime factorization method to determine the square root of 1225 with complete explanation.

What is the Value of Square Root of 1225?

If a number is multiplied by itself and gives the result as 1225, then we can say that the number is the square root 1225. Symbolically, the square root of 1225 is expressed as √1225, which is the radical form of the square root of 1225.

Hence, √1225 = √(Number × Number)

Hence, by multiplying the number 35 for two times, we get the original number 1225.

(i.e) √1225 = √(35× 35)

√1225 = √(35)²

On removing square and square root, we will get

√1225 = ± 35

Square Root of 1225 by Prime Factorization Method

The square root of 1225 can be found using the prime factorization method. To find the value, we should know the prime factorization of 1225. Thus, the prime factorization of a number 1225 is 5² × 7².

Thus, √1225 = (√5)². (√7)²

√1225 = 5×7

√1225 = 35

Hence, the square root of 1225 is equal to 35.

Square Root of 1225 by Long Division Method

The steps to obtain the square root of 1225 using the long division method is provided as follows:

Step 1: First, write the number 1225. Next, Pair the number 1225 by putting the bar on the top of the number from right to left.

Step 2: Next, divide a number 12 by a number, such that the multiplication of the same number must be less than or equal to 12. Hence, 3×3=9, which is smaller than 12. Thus, we get quotient = 3 and remainder = 3.

Step 3: Double the quotient value, therefore we get 6 and let us take 60 as the new divisor. Now, bring down the number 25 for the division process. Thus, the new dividend obtained is 325. Now, determine the number, such that (60 + new number) × new number will give the product that should be smaller than or equal to 325. Hence, (60+5) × 5 = 325, which is equal to 325.

Step 4: Subtract 325 from 325, and we get 00 as the new reminder, and 35 as a quotient.

Step 5: Thus, the value of the square root of 1225, √1225 is 35.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify (√1225)/10

Solution:

Given: (√1225)/10.

As we know that the square root of 1225 is 35.

Substituting the value in the expression,

(√1225)/10 = 35/10

(√1225)/10 = 3.5

Therefore, the simplification of (√1225)/10 is 3.5.

Example 2:

Compute the value of a, if a√1225 = 105.

Solution:

Given: a√1225 = 105 …(1)

We know that √1225 = 35

Now, substitute the value in equation (1), we get

a(35) = 105

a = 105/35

a = 3

Hence, the value of a is 3.

Example 3:

Simplify the expression: (√1225 × √1225) + 30

Solution:

Given expression: (√1225 × √1225) + 30

(√1225 × √1225) + 30 =(√1225)² +30

On removing square and square root, we get

(√1225 × √1225) + 30 = 1225 + 30

(√1225 × √1225) + 30 = 1255

Hence, the simplified form of (√1225 × √1225) + 30 is 1255.