WAEC - Mathematics (2014 - No. 24)
Simplify \(\sqrt{\frac{8^2 \times 4^{n + 1}}{2^{2n} \times 16}}\)
16
8
4
1
Explanation
\(\sqrt{\frac{8^2 \times 4^{n + 1}}{2^{2n} \times 16}}\)
= \(\sqrt{\frac{2^{3(2)} \times 2^{2(n + 1)}}{2^{2n} \times 2^4}}\)
= \(\sqrt{\frac{2^6 \times 2^{2n + 2)}}{2^{2n} + 4}}\)
= \(\sqrt{\frac{2^6 + 2^{2n + 2)}}{2^{2n} + 4}}\)
= \(\sqrt{\frac{2^{2n + 8}}{2^{2n} + 4}}\)
= \(\sqrt{2^{2n + 8} \div 2^{2n} + 4}\)
= \(\sqrt{2^{2n - 2n} + 8 - 4}\)
= \(\sqrt{2^4}\)
= \(\sqrt{16}\)
= 4
= \(\sqrt{\frac{2^{3(2)} \times 2^{2(n + 1)}}{2^{2n} \times 2^4}}\)
= \(\sqrt{\frac{2^6 \times 2^{2n + 2)}}{2^{2n} + 4}}\)
= \(\sqrt{\frac{2^6 + 2^{2n + 2)}}{2^{2n} + 4}}\)
= \(\sqrt{\frac{2^{2n + 8}}{2^{2n} + 4}}\)
= \(\sqrt{2^{2n + 8} \div 2^{2n} + 4}\)
= \(\sqrt{2^{2n - 2n} + 8 - 4}\)
= \(\sqrt{2^4}\)
= \(\sqrt{16}\)
= 4
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