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TEA [102]
2 years ago
15

Help me with this question please

Mathematics
1 answer:
jeyben [28]2 years ago
4 0

Answer:

\dfrac{991}{40\sqrt{2}}

Step-by-step explanation:

Given expression:

\sqrt{72}-\dfrac{48}{\sqrt{50}}-\dfrac{45}{\sqrt{128}}+2\sqrt{98}

Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:

\implies \sqrt{36 \cdot 2}-\dfrac{48}{\sqrt{25 \cdot 2}}-\dfrac{45}{\sqrt{64 \cdot 2}}+2\sqrt{49 \cdot 2}

\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:

\implies \sqrt{36}\sqrt{2}-\dfrac{48}{\sqrt{25}\sqrt{2}}-\dfrac{45}{\sqrt{64}\sqrt{ 2}}+2\sqrt{49}\sqrt{2}

Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:

\implies \sqrt{6^2}\sqrt{2}-\dfrac{48}{\sqrt{5^2}\sqrt{2}}-\dfrac{45}{\sqrt{8^2}\sqrt{ 2}}+2\sqrt{7^2}\sqrt{2}

\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0

\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+2\cdot 7\sqrt{2}

Simplify:

\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+14\sqrt{2}

Combine like terms:

\implies 20\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}

Make the denominators of the two fractions the same:

\implies 20\sqrt{2}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}

Rewrite 20√2 as a fraction with denominator 40√2:

\implies 20\sqrt{2}\cdot\dfrac{40\sqrt{2}}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}

\implies \dfrac{1600}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}

Combine fractions:

\implies \dfrac{991}{40\sqrt{2}}

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