Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the square root of the following number by division method.
900
Find the number of digits in the square root of the following numbers (without any calculation).
390625
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.
1825
Find the squares of the following numbers using the identity (a + b)2 = a2 + 2ab + b2:
405
Find the squares of the following number using the identity (a + b)2 = a2 + 2ab + b2
1001
Find the square root the following by long division method:
390625
Find the square root of the following by long division method:
3226694416
Find the square root the following by long division method:
6407522209
Find the greatest 4-digit number which is a perfect square.
Find the square root of the following by long division method.
1.44
