Question

Find the smallest number by which 9408 must be divided so that the quotient is a perfect square. Find the square root of the quotient.​

Answer 1

$\huge\sf\pink{Answer}$

☞ 3 must be Divided and the Remainder is 56

━━━━━━━━━━━━━

$\huge\sf\blue{Given}$

✭ We are dividing 9408 with a number to make it a perfect square

━━━━━━━━━━━━━

$\huge\sf\gray{To \:Find}$

◈ The number to be divided?

━━━━━━━━━━━━━

$\huge\sf\purple{Steps}$

So first let's list out the factors of 9480 so here,

➝ 9408 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 7 × 7

So then let's pair two alike numbers here there are,

➢ 6 twos

➢ 2 sevens and

➢ 1 three

So here there is no pair for 3 and so if we divide 9408 by 3 we can get the perfect square

➳ $\sf\dfrac{9408}{3}$

➳ $\sf \red{3136}$

Now the quotient is,

➠ $\sf\sqrt{3136}$

➠ $\sf\orange{56}$

━━━━━━━━━━━━━━━━━━━