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Find two numbers which on multiplication …

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Find two numbers which on multiplication with √180 gives a rational number. Are these numbers rational are not?
  • 1 answers

Sia ? 6 years, 6 months ago

{tex}\sqrt { 180 } = \sqrt { 2 ^ { 2 } \times 3 ^ { 2 } \times 5 } = 6 \sqrt { 5 }{/tex}
On multiplying with {tex}\sqrt { 5 }{/tex} and 1, we get
{tex}6 \sqrt { 5 } \times \sqrt { 5 } \times 1 = 30{/tex}
{tex}\therefore{/tex}   {tex}\sqrt 5{/tex} and 1 are two numbers which on multiplication with {tex}\sqrt{180} {/tex} gives a rational number.
One is irrational and other is rational.

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