FIND THE LEAST NUMBER TO BE DIVIDED TO GET A PERFECT SQUARE

Problem 1 :

The least number, by which 1470 must be divided to get a number which is a perfect square, is:

a)   5    b)   6    c)   15     d)   30

Solution :

Prime factorization of 1470 is,

1470 = 2 × 3 × 5 × 7 × 7

We don't see pairs for 2, 3 and 5

2 × 3 × 5 = 30

So, 30 must be divided to 1470 to get a number which is perfect square.

So, option (d) is correct.

Problem 2 :

By which least number should 3087 be divided in order to get a perfect square?

Solution :

Prime factorization of 3087 is,

3087 = 3 × 3 × 7 × 7 × 7

3 has pair, 7 also has pair. But there is one more 7. So, 7 to be divided to make 3087 as perfect square.

Problem 3 :

A man plants 15376 apple trees in his garden and arranges them so that there are as many rows as there are apples trees in each row. The number of rows is 

(a)  124   (b) 126  (c) 134   (d) 144

Solution :

√15376

√15376 = √(2 x 2 x 2 x 2 x 31 x 31)

= 2 x 2 x 31

= 124

So, the number of rows is 124.

Problem 4 :

If 52/x = √(169/289), the value of x is 

(a) 52   (b) 58   (c) 62   (d) 68

Solution :

52/x = √(169/289)

52/x = √(13⋅13)//17⋅17)

52/x = 13/17

Doing cross multiplication, we get

13x =  52 (17)

x = 52(17)/13

x = 4(17)

x = 68

So, the value of x is 68.