Question

By which least number should each of the following numbers be multiplied to make them perfect squares (i) 3388

Answer 1

Answer:

154

Step-by-step explanation:

Therefore, we can write 3388=2×2×7×11×11 . Here we are dealing with a perfect square so we have to write the obtained factorization in the form of a group of two primes if possible. So, we can write 3388=(2×2)×7×(11×11)⋯⋯(1) . To find a perfect square root, we have to take one number from each group of two but here we can see that a single 7 cannot be written as a group of two.

Let us multiply by 7 on both sides of the equation (1) . So, we can write

3388×7=[(2×2)×7×(11×11)]×7

⇒3388×7=(2×2)×(7×7)×(11×11)

Here we can take one number from each group of two. So we will get the perfect square root. Hence, the required smallest number is 7 . Hence, 3388 should be multiplied by 7 to be a perfect square number.

Let us take one number from each group of two to find the square root. So, we can write

3388×7−−−−−−−√=2×7×11=154

Hence, 154 is square root of the perfect square number.