Evaluate: {75}+{18}-{27}

Correct Answer is : 23+32\;\;2{3}+3{2}23+32

Correct Answer is : 23+32\;\;2{3}+3{2}23+32

Test Index

BECE Mathematics 2024 Paper

Question : 11

Total: 40

Evaluate:

\sqrt{75}+\sqrt{18}-\sqrt{27}

Solution:

\sqrt{75}+\sqrt{18}\cdot\sqrt{27}

Note:

When simplifying surds, express the surd as a product of a perfect square and a number

\;2^2=4 \;\text{ and }\; \sqrt{4}=2

\;3^2=9 \;\text{ and }\; \sqrt{9}=3

\;4^2=16 \;\text{ and }\; \sqrt{16}=4

\;5^2=25 \;\text{ and }\; \sqrt{25}=5

\;6^2=36 \;\text{ and }\; \sqrt{36}=6

\;7^2=49 \;\text{ and }\; \sqrt{49}=7

\;8^2=64 \;\text{ and }\; \sqrt{64}=8

\;9^2=81 \;\text{ and }\; \sqrt{81}=9

\;10^2=100 \;\text{ and }\; \sqrt{100}=10

\;11^2=121 \;\text{ and }\; \sqrt{121}=11

\;12^2=144 \;\text{ and }\; \sqrt{144}=12

\;13^2=169 \;\text{ and }\; \sqrt{169}=13

\;14^2=196 \;\text{ and }\; \sqrt{196}=14

\;15^2=225 \;\text{ and }\; \sqrt{225}=15

\;75=25 \times 3

\;18=9 \times 2

\;27=9 \times 3

\;\sqrt{\overline{75}}+\sqrt{\overline{18}}\cdot\sqrt{27}=\sqrt{25\times 3}+\sqrt{9\times 2}\cdot\sqrt{9\times 3}

\;\sqrt{a\times \overline{b}}=\sqrt{a}\times\sqrt{b}

\;\sqrt{\overline{75}}+\sqrt{18}\cdot\sqrt{27}=\sqrt{25}\times\sqrt{3}+\sqrt{9}\times\sqrt{2}-\sqrt{9}\times\sqrt{3}

\;\sqrt{25}=5

\;\sqrt{\overline{9}}=3

\;\sqrt{\overline{75}}+\sqrt{\overline{18}}-\sqrt{27}=5\sqrt{3}+3\sqrt{2}-3\sqrt{3}

\;\sqrt{\overline{75}}+\sqrt{18}\cdot\sqrt{27}=5\sqrt{3}-3\sqrt{3}+3\sqrt{2}

\;\sqrt{75}+\sqrt{18}-\sqrt{27}=2\sqrt{3}+3\sqrt{2}

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