Question

2.   Find the smallest number by which 1800 must be multiplied so that it becomes a perfect square. Also find the square root of the perfect square so obtained.

Answer 1

factors = 3 x 3 x 3 x 10 x 10

Smallest number should be multiply = 3

√(3x3x3x3x10x10)  = 90 is square root of the perfect number

Answer 2

$\mathfrak{\huge{\orange{\underline{\red{Hola\: !}}}}}$

$\mathbb{\underline{\blue{Type\: Of\: Problem:}}}$

¶ To find the smallest number by which a No. (N) must be multiplied so that it becomes a perfect square.

$\mathbb{\underline{\blue{Approach\: To\: Problem:}}}$

• Resolve the No. into Product of Prime factors using prime factorisation
• Express the No. as product of prime factors in exponential form
• Identify the prime factors which are not having 2 as their powers
• Multiplying the product of No.s that do not contain 2 as their powers with No. gives the perfect square.
• The square root of this perfect square is product of all prime factors with 2 as their power.

$\mathcal{\underline{\blue{SOLUTION}}}$

Using prime factorisation,

2 | 1800
2 | 900
2 | 450
3 | 225
3 | 75
5 | 25
.• | 5

1800 = 2 × 2 × 2 × 3 × 3 × 5 × 5

$1800 = 2^{2} × 3^{2} × 5^{2} × 2$

•°• To make 1800 a perfect square,
it has to be multiplied by 2

1800 × 2 = 3600

•°•

$\underline{\underline{Required\: perfect\: square = 3600 }}$

Its square root = 2 × 2 × 3 × 5 = 600

$\underline{\underline{Required\: value\: Of\: square\: root = 600 }}$

$\mathfrak{\huge{\pink{Cheers}}}$

$\mathcal{\huge{\orange{Hope\: it\: Helps}}}$