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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.
Q 1: Find the least positive whole number with which 1458 should be multiplied so that the product is a perfect square, find the square root of that product.
Answer:

Q 2: Find the least positive whole number with which 405 should be multiplied so that the product is a perfect square.
Answer:

Q 3: Find the least positive whole number with which 243 should be multiplied so that the product is a perfect square.
Answer:

Q 4: Find the least positive whole number with which 1922 should be multiplied so that the product is a perfect square, find the square root of that product.
Answer:

Q 5: Find the least positive whole number with which 845 should be multiplied so that the product is a perfect square.
Answer:

Q 6: Find the least positive whole number with which 1568 should be multiplied so that the product is a perfect square.
Answer:

Q 7: Find the least positive whole number with which 605 should be multiplied so that the product is a perfect square, find the square root of that product.
Answer:

Q 8: Find the least positive whole number with which 288 should be multiplied so that the product is a perfect square, find the square root of that product.
Answer:

Question 9: This question is available to subscribers only!

Question 10: This question is available to subscribers only!


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