WAEC SSCE - General Mathematics - 2007…

Question 1 Report

Simplify $3\sqrt{45}-12\sqrt{5}+16\sqrt{20}$leaving your answer in surd form

$29\sqrt{5}$ Correct answer

$14\sqrt{15}$

$12\sqrt{15}$

$11\sqrt{5}$

Answer Details

First, we need to simplify each term under the square root sign. We can write: \begin{align*} 3\sqrt{45} &= 3\sqrt{9\times 5} = 3\times 3\sqrt{5} = 9\sqrt{5}\\ 12\sqrt{5} &= 2\times 2\times 3\sqrt{5} = 4\sqrt{5}\times 3\\ 16\sqrt{20} &= 16\sqrt{4\times 5} = 16\times 2\sqrt{5} = 32\sqrt{5} \end{align*} Now we can substitute these simplified expressions back into the original expression and simplify: \begin{align*} 3\sqrt{45}-12\sqrt{5}+16\sqrt{20} &= 9\sqrt{5}-4\sqrt{5}\times 3+32\sqrt{5}\\ &= (9-12+32)\sqrt{5}\\ &= 29\sqrt{5} \end{align*} Therefore, the answer is $29\sqrt{5}$.

Read lesson note on Fractions, Decimals, Approximations And Percentage (JAMB)






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WAEC SSCE - General Mathematics - 2007 (Objective)