Download App

Squares and Square Roots — Maths STD 8 — Question

Maharashtra BoardEnglish MediumSTD 8MathsSquares and Square Roots3 Marks
Question
Find the smallest number by which 3645 must be divided so that it becomes a perfect square. Also, find the square root of the resulting number.
✓

Answer

The prime factorisation of 3645,
3645 = 3 × 3 × 3 × 3 × 3 × 3 × 5
Grouping the factors into pairs of equal factors, we get,
3645 = (3 × 3) × (3 × 3) × (3 × 3) × 5
The factor, 5 does not have a pair. Therefore, we must divide 3645 by 5 to make a perfect square. The new number is,
(3 × 3) × (3 × 3) × (3 × 3) = 729
Taking one factor from each pair on the L.H.S, the square root of the new number is 3 × 3 × 3, which is equal to 27.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Mark Question" from Squares and Square Roots→Squares and Square Roots — all question types→Maths STD 8 question papers→Maharashtra Board STD 8 question papers→Maharashtra Board question paper generator→

Similar questions

A work force of 50 men with a contractor can finish a piece of work in 5 months. In how many months the same work can be completed by 125 men?
→
Hari bought 20kg of rice at Rs. 36/kg and 25kg of rice at Rs. 32/kg He mixed the two varieties and sold the mixture at Rs. 38/kg Find his gain percent in the whole transaction.
→
Divide 150 into three parts such that the second number is five-sixths the first and the third number is four-fifths the second.
→
Show that the following numbers is a perfect square. Also, find the number whose square is the given number in case:
$14641$
→
Evaluate $\sqrt{3}$ correct up to two places of decimal.
→
Find x, if
$\Big( \frac{3}{5}\Big)^{-3}\times\Big(\frac{3}{2}\Big)^{5}=\Big(\frac{3}{2}\Big)^{2\text{x}+1}$
→
By selling a flower pot for Rs. 322, a man gains 15%. At what price should he sell it to gain 20%?
→
Find the value of x for which $\Big(\frac{4}{9}\Big)^{4}\times\Big(\frac{4}{9}\Big)^{-7}=\Big(\frac{4}{9}\Big)^{2\text{x}-1}$
→
Devide The Following :
$\left(2 m^3+m^2+m+9\right) \div(2 m-1)$
→
Given that the number $\overline{67\text{y}19}$ is divisible by 9, where y is a digit, what are the possible valuse of y?
→