Advertisements
Advertisements
Question
By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.
Solution
Prime factors of 216 = 2 × 2 × 2 × 3 × 3 × 3
Grouping the factors into pairs of equal factors, we get
216 = 2 × 2 × 2 × 3 × 3 × 3
We find that there is no prime factor to form a pair with 2 and 3.
Therefore, we must divide the number by 6, so that the quotient becomes a perfect square.
If we divide the given number by 2 × 3 i.e. 6, then
New number = `216/6` = 36
Taking one factor from each, we get square root of new number (quotient)
= 2 × 3
= 6
APPEARS IN
RELATED QUESTIONS
Find the least number which must be added to the following number so as to get a perfect square. Also find the square root of the perfect square so obtained.
1750
Find the length of the side of a square whose area is 441 m2.
Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2:
599
Write the possible unit's digits of the square root of the following numbers\. Which of these number is odd square root?
9801
Find the square root the following by long division method:
9653449
Find the least number which must be subtracted from the following numbers to make them a perfect square:
194491
Find the square root of: `0.01 + sqrt(0.0064)`
Find the square root of the following by long division method.
1369
What is the least number that should be added to 6200 to make it a perfect square?
Find the least number of four digits that is a perfect square.
