Question

Given that √2 = 1.414 .Find the square root of 128

Can you please show me the steps

Answer 1

The square root of 128 is approximately 11.304. If we factor the square root of 128 to look for a perfect square we see that 2 *64 is a factor of 128. 64 is a perfect square. We can rewrite the square root of 128 as the square root of 64* the square root of 2. This will then simplify to 8 * the square root of 2. We then can estimate that the square root of 2 is bigger than the square root of 1 and less than the square root of 4 and is just a little less than halfway between them, so its approximate value is 1.4. Then multiply 8 * 1.4 and we get that the approximate value of the square root of 128 is 11.2 which is very close to the 11.304