**Find the least number should be multiplied to get a perfect square :**

Here we are going to see how to find the least number should be multiplied to get a perfect square.

For this, we use the method called prime factorization.

**Step 1 :**

Find the prime factors of the given number.

**Step 2 :**

To find the square root, we have to group the factors as pairs.

**Step 3 :**

By grouping the factors as pairs, we may find some of the numbers which do not have pairs. These are the required numbers to be multiplied in order make it as a perfect square.

**Example 1 :**

Find the least number by which 200 must be multiplied to make it a perfect square.

**Solution :**

**Step 1 :**

Let us find the prime factors of 200 using the method prime factorization.

**Step 2 :**

200 = 2 ⋅ 2 ⋅ 2 ⋅ 5 ⋅ 5

**Step 3 :**

‘2’ remains without a pair.

Hence, 200 must be multiplied by 2 to make it a perfect square.

**Example 2 :**

Find the smallest whole number by which the following number should be multiplied so as to get a perfect square.Also find the square root of the number so obtained.

252

**Solution :**

**Step 1 :**

Let us find the prime factors of 252 using the method prime factorization.

**Step 2 :**

252 = 2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 7

**Step 3 :**

‘7’ remains without a pair.

Hence, 252 must be multiplied by 7 to make it a perfect square.

√(252 ⋅ 7) = √(2 ⋅ 2 ⋅ 3 ⋅ 3 ⋅ 7 ⋅ 7)

√1764 = 2 ⋅ 3 ⋅ 7 = 42

**Example 3 :**

Find the smallest whole number by which the following number should be multiplied so as to get a perfect square.Also find the square root of the number so obtained.

180

**Solution :**

**Step 1 :**

Let us find the prime factors of 180 using the method prime factorization.

**Step 2 :**

180 = 2 ⋅ 2 ⋅ 5 ⋅ 3 ⋅ 3

**Step 3 :**

‘5’ remains without a pair.

Hence, 180 must be multiplied by 5 to make it a perfect square.

√(180 ⋅ 5) = √(2 ⋅ 2 ⋅ 5 ⋅ 3 ⋅ 3 ⋅ 5)

√900 = 2 ⋅ 5 ⋅ 3 = 30

- How to find the number of digits of square root of a number
- Find the least number to be added to get a perfect square
- How to find the least number to be subtracted to get a perfect square
- Find the least number should be multiplied to get a perfect square
- Find the least number should be divided to get a perfect square

After having gone through the stuff given above, we hope that the students would have understood "Find the least number should be multiplied to get a perfect square"

Apart from the stuff given above, if you want to know more about "Find the least number should be multiplied to get a perfect square", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**