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This is the second of our many quizzes on simplifying square roots. Click on this to access more such competitive quizzes on squares and square roots.

Simplifying Square Roots Quiz 2

mathematics

 Simplify $\dfrac{{\sqrt {19044} }}{{\sqrt {4761} }} + \dfrac{{\sqrt {53361} }}{{\sqrt {5929} }} - \dfrac{{\sqrt {15129} }}{{\sqrt {1681} }}$

 Simplify the square roots and determine the final value using BODMAS

 $\text{On simplifying the roots we get,} \\ \Rightarrow \dfrac{{138}}{{69}} + \dfrac{{231}}{{77}} - \dfrac{{123}}{{41}} \\\Rightarrow 2 + 3 - 3 \\\Rightarrow 2$ 

 Simplify $\dfrac{1}{{\sqrt {1681} }} \times \dfrac{1}{{\sqrt {2401} }} \times \dfrac{1}{{\sqrt {1369} }} \div \dfrac{1}{{\sqrt {82369} }}$

  $\text{On simplifying the roots we get,}\\ \Rightarrow \dfrac{1}{{41}} \times \dfrac{1}{{49}} \times \dfrac{1}{{37}} \div \dfrac{1}{{287}} \\\Rightarrow \dfrac{1}{{41}} \times \dfrac{1}{{49}} \times \dfrac{1}{{37}} \times 287 \\\Rightarrow \dfrac{1}{{259}}$

 Simplify $\sqrt {1444}  + \dfrac{1}{{\sqrt {2809} }} - \dfrac{1}{{\sqrt {11236} }} + {\sqrt {46656} ^{\frac{1}{3}}}$

  $\text{On simplifying the roots we get,} \\\Rightarrow 38 + \dfrac{1}{{53}} - \dfrac{1}{{106}} + {216^{\frac{1}{3}}} \\\Rightarrow 38 + \dfrac{1}{{106}} + {\left\{ {{{\left( 6 \right)}^3}} \right\}^{\frac{1}{3}}} \\\Rightarrow 38 + \dfrac{1}{{106}} + 6 \\\Rightarrow \dfrac{{4665}}{{106}}$ 

 Simplify $\dfrac{{\sqrt {1156} }}{{\sqrt {10404} }} + \dfrac{{\sqrt {441} }}{{\sqrt {7056} }} + \dfrac{{\sqrt {289} }}{{\sqrt {7225} }} - \dfrac{{\sqrt {2304} }}{{\sqrt {9216} }} + \dfrac{{\sqrt {225} }}{{\sqrt {56.25} }}$

 $\text{On simplifying the roots we get,} \\ \Rightarrow \dfrac{{34}}{{102}} + \dfrac{{21}}{{84}} + \dfrac{{17}}{{85}} - \dfrac{{48}}{{96}} + \dfrac{{15}}{{7.5}} \\\Rightarrow \dfrac{1}{3} + \dfrac{1}{4} + \dfrac{1}{5} - \dfrac{1}{2} + 2 \\\Rightarrow \dfrac{{137}}{{60}}$ 

 Simplify $\dfrac{{\sqrt {2209} }}{{\sqrt {8836} }} \times \dfrac{{\sqrt {1521} }}{{\sqrt {24336} }} \times \dfrac{{\sqrt {2916} }}{{\sqrt {46656} }} \div \dfrac{{\sqrt {5184} }}{{\sqrt {20736} }} \div \dfrac{{\sqrt {196} }}{{\sqrt {49} }}$

 $\text{On simplifying the roots we get,}\\\Rightarrow \dfrac{{47}}{{94}} \times \dfrac{{39}}{{156}} \times \dfrac{{54}}{{216}} \div \dfrac{{72}}{{144}} \div \dfrac{{14}}{7} \\\Rightarrow \dfrac{1}{2} \times \dfrac{1}{4} \times \dfrac{1}{4} \div \dfrac{1}{2} \div 2 \\\Rightarrow \dfrac{1}{2} \times \dfrac{1}{4} \times \dfrac{1}{4} \times 2 \times \dfrac{1}{2} \\\Rightarrow \dfrac{1}{{32}}$ 