Simplify 3+sqrt(5)/7-3sqrt(5)

Question

ScanSolve AI Tutor · Accepted Answer

Ili kurahisisha usemi huu, tunahitaji kuondoa mzizi wa mraba kutoka kwa denominator. Tunafanya hivyo kwa kuzidisha nambari na denominator kwa kiambishi cha denominator.

Zidisha nambari na denominator kwa kiambishi cha denominator.
Kiambishi cha $7-3\sqrt{5}$ ni $7+3\sqrt{5}$ .
$\frac{3+\sqrt{5}}{7-3\sqrt{5}} \times \frac{7+3\sqrt{5}}{7+3\sqrt{5}}$
Panua nambari.
$(3+\sqrt{5})(7+3\sqrt{5}) = 3(7) + 3(3\sqrt{5}) + \sqrt{5}(7) + \sqrt{5}(3\sqrt{5})$ $= 21 + 9\sqrt{5} + 7\sqrt{5} + 3(\sqrt{5})^2$ $= 21 + 16\sqrt{5} + 3(5)$ $= 21 + 16\sqrt{5} + 15$ $= 36 + 16\sqrt{5}$
Panua denominator.
Tumia tofauti ya fomula ya mraba: $(a-b)(a+b) = a^2 - b^2$ .
$(7-3\sqrt{5})(7+3\sqrt{5}) = 7^2 - (3\sqrt{5})^2$ $= 49 - (3^2 \times (\sqrt{5})^2)$ $= 49 - (9 \times 5)$ $= 49 - 45$ $= 4$
Unganisha nambari na denominator zilizorahisishwa.
$\frac{36 + 16\sqrt{5}}{4}$
Rahisisha sehemu kwa kugawanya kila neno katika nambari kwa denominator.
$\frac{36}{4} + \frac{16\sqrt{5}}{4}$ $9 + 4\sqrt{5}$

Simplify 3+sqrt(5)/7-3sqrt(5)

Answer

Step-by-step solution

Zidisha nambari na denominator kwa kiambishi cha denominator.

Panua nambari.

Panua denominator.

Unganisha nambari na denominator zilizorahisishwa.

Rahisisha sehemu kwa kugawanya kila neno katika nambari kwa denominator.

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