Math Word Problems - GED, PSAT, SAT, ACT, GRE Preparation 3.18 Word Problems On Square Roots - I

A number whose square root is a rational number is called a perfect square number.

Procedure: Example:
Find the least positive whole number with which 125 should be multiplied so that the product is a perfect square, and also find the square root of that product. Solution:
Write 125 as product of prime factors.
125 = 5*25
=5*5*5
=(5*5)*5
Therefore, the given number should be multiplied by 5 to make it a perfect square number.
The required positive integer is 5.
The product so obtained = 125*5 =5*5*5*5 = (5*5)^{2}
The square root of 125*5 is 5*5
√625 = 25.

Direction: Solve the following problems. Write 5 examples of your own.