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Find the smallest natural number by …

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Find the smallest natural number by which 1,200 should be multiplied so that the square root of the product is a rational number

Posted by Kashish Agarwal 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

1200 = {tex}4 \times 3 \times ( 2 \times 5 ) ^2{/tex}
{tex}= 3 \times 2 ^ { 2 } \times 2 ^ { 2 } \times 5 ^ { 2 }{/tex}
{tex}= 3 ^ { 1 } \times \left( 2 ^ { 2 } \times 5 \right) ^ { 2 }{/tex}
Multiplying with 3 we get
{tex}3 ^ { 2 } \times \left( 2 ^ { 2 } \times 5 \right) ^ { 2 } = ( 3 \times 4 \times 5 ) ^ { 2 } = 60 ^ { 2 }{/tex}
The required smallest natural number is 3.

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CBSE > Class 10 > Mathematics