Rationalize the denominator and simplify 2√5 √5+2

Question

ScanSolve AI Tutor · Accepted Answer

Ili kurahisisha na kuondoa mizizi kwenye denominata, tunazidisha namba na denominata kwa conjugate ya denominata. Conjugate ya $\sqrt{5} + 2$ ni $\sqrt{5} - 2$ .

Zidisha namba na denominata kwa conjugate.
$\frac{2\sqrt{5}}{\sqrt{5} + 2} \times \frac{\sqrt{5} - 2}{\sqrt{5} - 2}$
Panua namba na denominata.
Kwa namba:
$2\sqrt{5}(\sqrt{5} - 2) = (2\sqrt{5} \times \sqrt{5}) - (2\sqrt{5} \times 2)$ $= (2 \times 5) - 4\sqrt{5}$ $= 10 - 4\sqrt{5}$
Kwa denominata, tumia formula $(a+b)(a-b) = a^2 - b^2$ :
$(\sqrt{5} + 2)(\sqrt{5} - 2) = (\sqrt{5})^2 - (2)^2$ $= 5 - 4$ $= 1$
Weka matokeo pamoja.
$\frac{10 - 4\sqrt{5}}{1}$ $= 10 - 4\sqrt{5}$
Jibu la mwisho ni:
$10 - 4\sqrt{5}$

Rationalize the denominator and simplify 2√5 √5+2

Answer

Step-by-step solution

Zidisha namba na denominata kwa conjugate.

Panua namba na denominata.

Weka matokeo pamoja.

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