# Find the Smallest Number by Which 10368 Be Divided, So that the Result is a Perfect Square. Also, Find the Square Root of the Resulting Numbers. - Mathematics

Sum

Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers.

#### Solution

10368 = bar(2xx2) xx bar(2xx2) xx bar(2xx2) xx2 xx bar(3xx3) xx bar(3xx3)

On grouping the prime factors of 10368 as shown; one factors i.e. 2 is left which cannot be paired with equal factor.

 2 10368 2 5184 2 2592 2 1296 2 648 2 324 2 162 3 81 3 27 3 9 3

∴ The given number should be divided by 2.

Now sqrt(10368/2)

= sqrt((bar(2xx2) xxbar(2xx2) xx bar(2xx2) xx2 xx bar(3xx3) xx bar(3xx3))/(2)

= 2 x 2 x 2 x 3 x 3 = 72

Is there an error in this question or solution?

#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 3 Squares and Square Root
Exercise 3 (A) | Q 4 | Page 38