Question

Which is the smallest number, with which 600 should be multiplied so that it becomes a perfect square?​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, we are asked to find the smallest number, with which 600 should be multiplied so that it becomes a perfect square.

So, at first we'll resolve the given number into prime factors by using prime factorization method. After that, we'll make the pairs of common factors. The number which can't be grouped into pairs is the smallest number, with which 600 should be multiplied so that it becomes a perfect square.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

Resolving 600 into prime factors,

$\large \begin{array}{ c| c} \underline{ \sf{2}} & \underline{ \sf{600}} \\\underline{ \sf{2}} & \underline{ \sf{300}} \\ \underline{ \sf{3}} & \underline{ \sf{150}} \\ \underline{ \sf{2}} & \underline{ \sf{50}} \\\underline{ \sf{5}} & \underline{ \sf{25}} \\ \underline{ \sf{5}} & \underline{ \sf{5}} \\ \: &1 \end{array}$

We get that,

$\longrightarrow$ 600 = 2 × 2 × 3 × 2 × 5 × 5

• Now, make the pairs.

$\longrightarrow$ 600 = 2 × 2 × 3 × 2 × 5 × 5

We get that (3 × 2) left unpaired, so 6 is the smallest number, with which 600 should be multiplied so that it becomes a perfect square.

❝ Extra ❞

$\bf\red { \dag}$ How to find the square root of any number using prime factorization method ?

$\longmapsto$ In prime factorization method, firstly we find the prime factors of the given number by prime factorization. Then, we form pairs of like factors and from each pair we pick out one prime factor and then we multiply the the factors so picked , the product we get is the square root of the given number.

Answer 2

Answer:

Step-by-step explanation:

Given,

The smallest number, with which 600 should be multiplied so that it becomes a perfect square.

Answer is 6.

Because, 6 × 600 = 3600

Square root of √3600 = √60 × √60 = (√60)^2 = 60

∴ 3600 is a perfect square

∴The smallest number = 6