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.
Advertisements
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 number of digits in the square root of the following numbers (without any calculation).
4489
Find the least number which must be subtracted from the following number so as to get a perfect square. Also find the square root of the perfect square so obtained.
825
Find the least number which must be subtracted from the following number so as to get a perfect square. Also find the square root of the perfect square so obtained.
4000
Find the squares of the following number using the identity (a + b)2 = a2 + 2ab + b2
1001
Find the square of the following number using the identity (a − b)2 = a2 − 2ab + b2:
599
Find the square root the following by long division method:
390625
Find the square root of the following by long division method:
3915380329
Find the value of `sqrt5` correct to 2 decimal places; then use it to find the square root of `(3-sqrt(5))/(3+sqrt(5)` correct to 2 significant digits.
Find the least number that must be subtracted to 6666 so that it becomes a perfect square. Also, find the square root of the perfect square thus obtained
