Radicals
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[tex]\Large \bold{1. \ \ \green{\sqrt[3]{320x^{15} y^{17}}} \ \ or \ \ \red{\sqrt[3]{320} x^{15} y^{17}}}[/tex]
(Dalawa po ang solution na binigay ko kasi di po tugma yung given radical expression sa question mo at nung nasa pic)
[tex]\large \begin{aligned} \sf Solution: \ & \tt \green{\sqrt[3]{320x^{15} y^{17}}} \\ =& \tt \sqrt[3]{4^3 \times 5x^{15} \times y^{15} \times y^2} \\ =& \tt \sqrt[3]{4^3} \sqrt[3]{x^{15}} \sqrt[3]{y^{15}} \sqrt[3]{5y^2} \\ =& \boxed{\bold{\purple{\Large 4x^5y^5 \sqrt[3]{5y^2}}}} \end{aligned}[/tex]
[tex]\large \begin{aligned} \sf Solution: \ & \tt \red{\sqrt[3]{320} x^{15} y^{17}} \\ =& \tt \sqrt[3]{4^3 \times 5} x^{15} y^{17} \\ =& \boxed{\bold{\purple{\Large 4\sqrt[3]{5}x^{15}y^{17}}}} \end{aligned}[/tex]
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[tex]\Large \bold{2. \ \ \green{\frac{5}{5- \sqrt{2}}} \ \ or \ \ \red{\frac{5}{5}- \sqrt{2}}}[/tex]
(Di rin tugma ang given mo dito)
[tex]\large \begin{aligned} \sf Solution: \ & \tt \green{\frac{5}{5- \sqrt{2}}} \\ =& \tt \frac{5}{5- \sqrt{2}} \times \frac{5+ \sqrt{2}}{5+ \sqrt{2}} \\ =& \tt \frac{5(5+ \sqrt{2})}{(5- \sqrt{2})(5+ \sqrt{2})} \\ =& \tt \frac{25+ 5\sqrt{2}}{25-2} \\ =& \boxed{\bold{\purple{\Large \frac{25+ 5\sqrt{2}}{23}}}} \end{aligned}[/tex]
[tex]\large \sf Solution: \ \tt \red{\frac{5}{5}- \sqrt{2}} = \boxed{\bold{\purple{\Large 1-\sqrt{2}}}}[/tex]
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[tex]\Large \bold{3. \ \ \frac{11}{8+ \sqrt{3}}}[/tex]
[tex]\large \begin{aligned} \sf Solution: \ & \tt \frac{11}{8+ \sqrt{3}} \\ =& \tt \frac{11}{8+ \sqrt{3}} \times \frac{8- \sqrt{3}}{8- \sqrt{3}} \\ =& \tt \frac{11(8- \sqrt{3})}{(8+ \sqrt{3})(8- \sqrt{3})} \\ =& \tt \frac{88-11\sqrt{3}}{64-3} \\ =& \boxed{\bold{\purple{\Large \frac{88-11\sqrt{3}}{61}}}} \end{aligned}[/tex]
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