InterviewSolution
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InterviewSolution
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Simplify the following (i) `sqrt45-3sqrt20+4sqrt5` (ii) `sqrt(24)/8 + sqrt54/9` (iii) `root4(12) xx root7(6)` (iv) `4sqrt28 div 3sqrt7 div root3(7)` (v)` 3sqrt3+2sqrt27 + 7/(sqrt3)` (vi) `(sqrt3-sqrt2)^(2)` (vii) `root4(81)-8root3(216)+15root5(32)+ sqrt225` (viii) `3/sqrt8+ 1 / sqrt2` (ix) `(2sqrt3)/3- (sqrt3)/6` |
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Answer» `sqrt45-3sqrt20+4sqrt5= sqrt(3xx3xx5)-3sqrt(2xx2xx2)+4sqrt5` ` 3sqrt5-3xx2sqrt5+4sqrt5` `3sqrt5-6sqrt5+4sqrt5=sqrt5` `sqrt24/8+sqrt54/9=sqrt(2xx2xx2xx2xx3)/8+sqrt(3xx3xx3xx2)/9` `(2sqrt6)/8 + (3sqrt6)/9=sqrt6/4+sqrt6/3` `(3sqrt6+4sqrt6)/12=(7sqrt6)/12` `root4(12)xxroot7(6)=(12)^(1//4)xx(6)^(1//7)` `(2xx2xx3)^(1//4)xx(2xx3)^(1//7)=2^(1//4).2^(1//4).3^(1//4).2^(1//7).3^(1//7)` `2^(1/4+1/4+1/7)xx3^(1/4+1/7)` `2^(9//14)xx3^(11//28)=root14(2^(9))root28(3^(11)) " " [ x^(m).x^(n)=x^(m+n)]` `root28(2^(18))root28(33^(11))=root28(2^(18)xx3^(11)) " " [ root na= root(mn)(a^(m))` (iv) `4sqrt28+3sqrt7 div root3(7) =(4sqrt(4xx7)div3sqrt7)divroot3(7)` ` ((8sqrt7)/(3sqrt7))div(7)^(1/3)` `8/3div7^(1/3)= 8/(3root3(7))` (v) `3sqrt3+2sqrt27+7/sqrt3=3sqrt3+2sqrt(3xx3xx3)+7/sqrt3xxsqrt3/sqrt3` `3sqrt3+ 6sqrt3+(7sqrt3)/3=9sqrt3+(7sqrt3)/3` `3sqrt3+6sqrt3+(7sqrt3)/3=9sqrt3+(7sqrt3)/3` `(27sqrt3+7sqrt3)/3=(34sqrt3)/3` (vi) `(sqrt3-sqrt2)^(2)+(sqrt2)^(2)-2sqrt3xxsqrt2 ` [ using identity , `(a-b)^(2)= a^(2+b^(2)-2ab]` `3+2-2sqrt(3xx2)=5-2sqrt6` (vii) `root4(81)-8root3(216)+15root5(32)+sqrt225` `(81)^(1/4)-8xx(6^(3))^(1/3)15xx(32)^(1/5)+sqrt((15)^(2))` ` (3^(4))^(1/4)-8xx(6^(3))^(1/3)+15xx2^(5xx(1/5))+15` `3^(1)-8xx6^(1)+15xx2^(1)+15` 3-48+30+15 48-48=0 `3/sqrt8+1/sqrt2=3/(sqrt(2xx2xx2))+1/sqrt2=3/(2sqrt2)+1/sqrt2` ` (3+2)/(2sqrt2)+1/sqrt2` `(5sqrt2)/(2xx2)=5/(2sqrt2)xxsqrt2/sqrt2` `(5sqrt2)/(2xx2)=(5sqrt2)/4` (ix) `(2sqrt3)/3-sqrt3/6=(4sqrt3-sqrt3)/6=(3sqrt3)/6=sqrt3/2` |
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