Question

what would be the denominator after rationalising 7/(5 root3 -(5 root2? options: a.19 b.20 c.25. d.none of these​

Answer 1

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Topic - Rationalisation of denominator

Question -

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \large \dag \: \: \pink{ \frac{7}{5 \sqrt{3} - 5 \sqrt{2} }} \: \: \large \dag$

Answer -

Option3️⃣$\bigg)$ 25

Your Solution -

$\rm {Rationalising \: factor \: of \: \red{ (5 \sqrt{3} - 5 \sqrt{2})} \: \: \: is \: \: \red{( 5 \sqrt{3} + 5 \sqrt{2)} }} \\ \\ = \frac{7}{5 \sqrt{3} - 5 \sqrt{2} } \times \frac{5 \sqrt{3} + 5 \sqrt{2} }{5 \sqrt{3} + 5 \sqrt{2} } \\ \\ = \frac{ 7(5 \sqrt{3} + 5 \sqrt{2} )}{ {(5 \sqrt{3} )}^{2} - (5 \sqrt{2} )^{2} } \\ \\ = \frac{35 \sqrt{3} + 35 \sqrt{2} }{75 - 50} \\ \\ \: = \frac{35 \sqrt{3} + 35 \sqrt{2} }{25} \red{ [Answer]} \\ \rm\pink{OR} \\ = \frac{ \cancel5(7 \sqrt{3} + 7 \sqrt{2} )}{ \cancel{25} \: _5} \\ \\ = \frac{7 \sqrt{3} + 7 \sqrt{2} }{5}\red{ [Answer ] }$

Steps or formula need + Additional information

• ( a - b ) ( a + b ) = a² - b²

• ( a + b )² = a² + b² + 2ab

• ( a - b )² = a² + b² - 2ab

• Rationalising factor is the opposite term of the denominator.

• Suppose we are given a number whose denominator is irrational. Then, the process of converting it into an equivalent expression whose denominator is a rational number by multiplying its numerator and denominator by a suitable number is called rationalisation.

• (5√3)² = (5×5)(√3 × √3) = (25)(√9) = 25 × 3 = 75

• ( 5√2)² = (5×5)(√2×√2) = (25)(√4)=25×2 = 50

• For rationalising the denominator of a number, we multiply its numerator and denominator by its rationalising factor.