Question

Find the least number by which 58,800 should be multiplied to get a perfect square.​

Answer 1

Answer:

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Step-by-step explanation:

Find the least number should be multiplied to get a perfect square :

Here we are going to see how to find the least number should be multiplied to get a perfect square.

For this, we use the method called prime factorization.

Step 1 :

Find the prime factors of the given number.

Step 2 :

To find the square root, we have to group the factors as pairs.  

Step 3 :

By grouping the factors as pairs, we may find some of the  numbers which do not have pairs. These are the required numbers to be multiplied in order make it as a perfect square.

Example 1 :

Find the least number by which 200 must be multiplied to make it a perfect square.

Solution :

Step 1 :

Let us find the prime factors of 200 using the method prime factorization.

Step 2 :

200  =  2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5

Step 3 :

‘2’ remains without a pair.

Hence, 200 must be multiplied by 2 to make it a perfect square.

Example 2 :

Find the smallest whole number by which the following number should be multiplied so as to get a perfect square.Also find the square root of the number so obtained.

252

Answer 2

Step-by-step explanation:

LCM of 58800 = 2×2×2×2×5×5×7×7×3

we should multiply by 3 on both sides to get a perfect square

58800×3 = 2×2×2×2×5×5×7×7×3×3

176400. = 176400

176400 is a perfect square

176400 = (420)²

so 3 should be multiplied to get a perfect square