Question

What is the square root of 117, show your work.

Answer 1

Answer:10.816

Step-by-step explanation:

Step 1: First, we will pair the digits of 117 from right to left. Place a horizontal bar to indicate the pairs. 17 is one such pair, which leaves 1 as a single digit in the other pair.

Step 2: Now we will find a number which on multiplication with itself gives a product that is less than or equal to 1. We know, 1 × 1 = 1.

Step 3: Now, we bring down 17 and multiply the quotient by 2. This gives us 2. Hence, 2 is the starting digit of the new divisor.

Step 4: 0 is placed at the units place of the new divisor because when 20 is multiplied by 0, we get 0. The answer obtained now is 17 and we bring down 00.

Step 5: The quotient now becomes 10 and it is multiplied by 2. This gives 20, which becomes the starting digits of the new divisor.

Step 6: 8 is placed at the units place of the new divisor because on multiplying 208 by 8 we get 1664. The remainder obtained is 36 and we bring 00 down.

Step 7: The quotient 108 when multiplied by 2 gives 216, which will be the starting digits of the new divisor.

Step 8: 1 is placed at the units place of the divisor because on multiplying 2161 by 1, we will get 2161. The answer obtained is 1439. Next, we will bring down the next pair of numbers, 00.

Step 9: The quotient 1081 when multiplied by 2 gives 2162, which will be the starting digits of the new divisor.

Step 10: 6 is placed at the units place of the divisor because on multiplying 21626 by 6, we will get 129756. The remainder obtained is 14144. We can bring 00 down and repeat these steps until we get the number we want.

Answer 2

Answer:

It's approximately equal to 13.3.

Solution:

• The square root of 117 is a surd, meaning that it can't be expressed as a fraction (in p/q form).
• The square root of 117 is equal to
• 13.3 (rounded to the nearest tenth)

Hope it helps.

Do comment if you have any query.