Question

Simplify the expression ✓ 135.135 =

Answer 1

The given expression is :

`\sqrt[]{135}`

To find the square root of 135 :

1) Group the digits into pair : 135 will be 01 35

Now perform the division :

Find the largest number whose square is less than or equal to the number in the leftmost group (11 = 1). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (01). Divide and get the remainder (0 in this case).

Bring down the next pair 35. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 21 × 1 = 21, so we choose the new digit as 1. Get the remainder.

Now, Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 226 × 6 = 1356, so we choose the new digit as 6. Get the remainder.

Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 2321 × 1 = 2321, so we choose the new digit as 1. Get the remainder.

Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. In this case 23228 × 8 = 185824, so we choose the new digit as 8. Get the remainder.

End the division upto three decimal places So

`\sqrt[]{135}=11.618`

Answer :

`\sqrt[]{135}=11.618`