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(1) Evaluate :  (i)    \sqrt{45}\times\sqrt{20}       (ii)  .  \frac{\sqrt{720}}{\sqrt{320}}

Soln. (i) \sqrt{45}\times \sqrt{20}  = \sqrt{45\times20}  =  \sqrt{9\times5\times5\times4} =  (3 \times  5 \times  2) = 30.

 (ii) \frac{\sqrt{720}}{\sqrt{320}} =  \sqrt{\frac{720}{320}} =  \sqrt{\frac{144}{64}} =  \frac{12}{8} = \frac{3}{2} .

 

(2) If  \sqrt{28} = 5.2915,  find the value of \sqrt{\frac{4}{7}} .

Solution. \sqrt{\frac{4}{7}} = \sqrt{\frac{4}{7}\times \frac{7}{7}}  =  \frac{\sqrt{28}}{7} =  \frac{5.2915}{7} = 0.7559.

 

(3) If  \sqrt{21} = 4.5826, find the value of   \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}.

Soln. \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} =  \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}} \times \frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}}

=\frac{\left (\sqrt{7}+\sqrt{3} \right )^{2}}{\left (7-3 \right )}

=\frac{7+3+2\sqrt{7}\times\sqrt{3}}{4}

= \frac{10+2\sqrt{21}}{4} = \frac{5}{2} +\frac{\sqrt{21}}{2}

= 2.5 + 2.2913

= 4.7913.

 

(4) Find the value of  :  \sqrt{\frac{.16\times .064 \times .081}{.036\times.049\times .25} }

Soln. The sum of  decimal places in numerator and denominator of  the radicand being the same, we may remove the decimal places.

\therefore Given Exp. = \sqrt{\frac{16\times 64 \times 81}{36\times49\times 25} } = \frac{4\times8\times9}{6\times7\times5} = \frac{48}{35}.

 

(5) If  \sqrt{\frac{x}{196}} = \frac{65}{26} ,  find the value of  x.

Solution. Squaring on both the sides, we get :

\frac{x}{196} =  \frac{65}{26} \times \frac{65}{26}  .      So, x  = \left (\frac{65}{26} \times\frac{65}{26} \times 196 \right ) =  1225.

 

(6) If   \left (1+\frac{x}{12} \right )=\sqrt{1+\frac{81}{144}}  ,  find the value of  x.

Solution. The given equation is : \left (1+\frac{x}{12} \right )=\sqrt{1+\frac{81}{144}}

or  \left (1+\frac{x}{12} \right )  =  \frac{15}{12}  or  \frac{x}{12}   =  \left (\frac{15}{12}-1 \right )    or   \frac{x}{12}=\frac{3}{12}

So,  x  =  3.

 

Best of Luck…

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