rationalise this. 4/2+√3+√7
Minniepie:
Is the question 4/(2+√3×√7)
no it's 4/2+√3+7
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Sol:
4 / (2 + √3 + √7)
= 4/[(2 + √3) + √7]
Rationalising factor of the denominator is [(2 + √3) - √7]
= 1/[(2 + √3) - √7] x [(2 + √3) - √7] / [(2 + √3) - √7]
= [(2 + √3) - √7] / [(2 + √3)2 - 7]
= [(2 + √3) - √7] / [4 + 4√3 + 3 - 7]
= [(2 + √3) - √7] / [4√3]
Rationalising factor of the denominator is √3.
= [(2 + √3) - √7] / [√3] x [√3/√3]
= [√12 + 3 - √21] / 3
Hence, the fraction with a rational denominator is [√12 + 3 - √21] / 3.
4 / (2 + √3 + √7)
= 4/[(2 + √3) + √7]
Rationalising factor of the denominator is [(2 + √3) - √7]
= 1/[(2 + √3) - √7] x [(2 + √3) - √7] / [(2 + √3) - √7]
= [(2 + √3) - √7] / [(2 + √3)2 - 7]
= [(2 + √3) - √7] / [4 + 4√3 + 3 - 7]
= [(2 + √3) - √7] / [4√3]
Rationalising factor of the denominator is √3.
= [(2 + √3) - √7] / [√3] x [√3/√3]
= [√12 + 3 - √21] / 3
Hence, the fraction with a rational denominator is [√12 + 3 - √21] / 3.
why you have taken rationalising factor of 2+√3-7
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