(i) Let E=4√3
For rationalising the denominator, multiply numerator and denominator by √3. We get,
E=4√3×√3√3=4√33=43×1.732=6.39283=2.309 [Put √3=1.732]
(ii) For rationalising denominator, multiply numerator and denominator by √6. We get,
E=6√6×√66=6√66=√2×√3=1.414×1.732=2.449 [Put √2=1.414 and √3=1.732]
(iii) Let E=√10−√52=√5√2−√52=√5(√2−1)2 [∵√10=√2√5]
=2.236(1.414−1)2=1.118×0.414=0.46285≅0.463
(iv) Let E=√22+√2
For rationalizing the denominator, multiply numerator and denominator by 2−√2.
We get,
=√22+√2×2−√22−√2=√2(2−√2)(2)2−(√2)2
[Using identity, (a−b)(a+b)=a2−b2]
=√2×√2(√2−1)2=2(√2−1)2=√2−1=1.414=0.414 [Put√2=1.414]
(v)
Let E=1√3+√2
For rationalising the denominator multiply numerator and denominator by √3−√2.
We get,
1√3+√2×√3−√2√3−√2=√3−√2(√3)2−(√2)2
[Using identity,(a−b)(a+b)=a2−b2]
=√3−√23−2=√3−√2
=1.732−1.414=0.318 [Put √3=1.732 and √2=1.414]