Rationalize the denominators of the following: (i) 1/√7 (ii) 1/(√7√6) (iii) 1/(√5+√2) (iv) 1/(√72)
Rationalize the denominators of the following:
(i) 1/√7
(ii) 1/(√7√6)
(iii) 1/(√5+√2)
(iv) 1/(√72)
(i) 1/√7
Multiply and divide 1/√7 by √7
(1×√7)/(√7×√7) = √7/7
(ii) 1/(√7√6)
Multiply and divide 1/(√7√6) by (√7+√6)
[1/(√7√6)]×(√7+√6)/(√7+√6) = (√7+√6)/(√7√6)(√7+√6)
= (√7+√6)/√7^{2}√6^{2 }[denominator is obtained by the property, (a + b)(a  b) = a^{2}b^{2}]
= (√7+√6)/(76)
= (√7+√6)/1
= √7+√6
(iii) 1/(√5+√2)
Multiply and divide 1/(√5+√2) by (√5√2)
[1/(√5+√2)]×(√5√2)/(√5√2) = (√5√2)/(√5+√2)(√5√2)
= (√5√2)/(√5^{2}√2^{2}) [denominator is obtained by the property, (a+b)(ab) = a^{2}b^{2}]
= (√5√2)/(52)
= (√5√2)/3
(iv) 1/(√72)
Multiply and divide 1/(√72) by (√7+2)
1/(√72)×(√7+2)/(√7+2) = (√7+2)/(√72)(√7+2)
= (√7+2)/(√7^{2}2^{2}) [denominator is obtained by the property, (a+b)(ab) = a^{2}b^{2}]
= (√7+2)/(74)
= (√7+2)/3

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