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PSLE Foundation Mathematics

Simplify $\sqrt{75}-2\sqrt{12}+\sqrt{27}$.

Simplifying Surds

Simplifying like surds

Surds

<p>Simplify ${{\left( \sqrt{6}+\sqrt{7} \right)}^{94}}\times {{\left( 2\sqrt{42}-13 \right)}^{47}}$.</p>

Simplify ${{\left( \sqrt{6}+\sqrt{7} \right)}^{94}}\times {{\left( 2\sqrt{42}-13 \right)}^{47}}$.

<p>Without the use of a calculator, simplify $\sqrt{8}+\sqrt{18}$.</p>

Without the use of a calculator, simplify $\sqrt{8}+\sqrt{18}$.

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\frac{\sqrt{75}\times \sqrt{72}}{\sqrt{24}}$</div></li><li><div class="list-item-paragraph">$\frac{4}{5\sqrt{2}}$</div></li><li><div class="list-item-paragraph">$\sqrt{32}+\sqrt{50}$</div></li><li><div class="list-item-paragraph">$\left( 7+2\sqrt{3} \right)\left( 5-\sqrt{3} \right)$</div></li></ol>

Simplify each of the following surds without using a calculator.

$\frac{\sqrt{75}\times \sqrt{72}}{\sqrt{24}}$

$\left( 7+2\sqrt{3} \right)\left( 5-\sqrt{3} \right)$

Rationalising Denominators

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{50}$</div></li><li><div class="list-item-paragraph">$\sqrt{7}\times \sqrt{14}$</div></li><li><div class="list-item-paragraph">$\sqrt{27}\times \sqrt{2}$</div></li><li><div class="list-item-paragraph">$\frac{\sqrt{343}}{\sqrt{7}}$</div></li></ol>

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{75}+\sqrt{108}$</div></li><li><div class="list-item-paragraph">$\sqrt{32}+\sqrt{50}$</div></li><li><div class="list-item-paragraph">$\left( 3+5\sqrt{2} \right)\left( 4-\sqrt{2} \right)$</div></li></ol>

$\left( 3+5\sqrt{2} \right)\left( 4-\sqrt{2} \right)$

Addition and Subtraction of Surds

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li data-list-item-id="item-1759570666193-i6sd8zfcz" data-list-item-path="item-1759570666193-i6sd8zfcz"><div class="list-item-paragraph">$\frac{\sqrt{125}}{\sqrt{10}}$</div></li><li data-list-item-id="item-1759570666755-mqmhsy7eh" data-list-item-path="item-1759570666755-mqmhsy7eh"><div class="list-item-paragraph">$\frac{\sqrt{80}\times \sqrt{12}}{\sqrt{5}}$</div></li><li data-list-item-id="item-1759570669883-0bktcn8ub" data-list-item-path="item-1759570669883-0bktcn8ub"><div class="list-item-paragraph">$\frac{10}{3\sqrt{5}}$</div></li></ol>

$\frac{\sqrt{80}\times \sqrt{12}}{\sqrt{5}}$

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{8}\times \sqrt{5}$</div></li><li><div class="list-item-paragraph">$\sqrt{20}\times \sqrt{16}$</div></li><li><div class="list-item-paragraph">$\sqrt{7}\times \sqrt{14}\times \sqrt{6}$</div></li></ol>

$\sqrt{7}\times \sqrt{14}\times \sqrt{6}$

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{40}$</div></li><li><div class="list-item-paragraph">$\sqrt{18}$</div></li><li><div class="list-item-paragraph">$\sqrt{396}$</div></li></ol>

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{720}+\sqrt{180}$</div></li><li><div class="list-item-paragraph">$\sqrt{48}+\sqrt{75}$</div></li><li><div class="list-item-paragraph">$\left( 3+7\sqrt{6} \right)\left( 5-\sqrt{6} \right)$</div></li></ol>

$\left( 3+7\sqrt{6} \right)\left( 5-\sqrt{6} \right)$

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\frac{\sqrt{27}}{\sqrt{15}}$</div></li><li><div class="list-item-paragraph">$\frac{\sqrt{40}\times \sqrt{12}}{\sqrt{3}}$</div></li><li><div class="list-item-paragraph">$\frac{15}{7\sqrt{3}}$</div></li></ol>

$\frac{\sqrt{40}\times \sqrt{12}}{\sqrt{3}}$

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{6}\times \sqrt{8}$</div></li><li><div class="list-item-paragraph">$\sqrt{12}\times \sqrt{36}$</div></li><li><div class="list-item-paragraph">$\sqrt{7}\times \sqrt{18}\times \sqrt{8}$</div></li></ol>

$\sqrt{7}\times \sqrt{18}\times \sqrt{8}$

<p>Simplify each of the following surds without using a calculator.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\sqrt{90}$</div></li><li><div class="list-item-paragraph">$\sqrt{12}$</div></li><li><div class="list-item-paragraph">$\sqrt{108}$</div></li></ol>

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