Question

simplify (under root 5 -2)2​

Answer 1

Answer:

$\left(\sqrt{5}-2\right)^2=9-4\sqrt{5}\quad \left(\mathrm{Decimal:\quad }\:0.05573\dots \right)$

Step-by-step explanation:

$\left(\sqrt{5}-2\right)^2$

$\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2$ $a=\sqrt{5},\:\:b=2$

$=\left(\sqrt{5}\right)^2-2\sqrt{5}\cdot \:2+2^2$

$\mathrm{Simplify}\:\left(\sqrt{5}\right)^2-2\sqrt{5}\cdot \:2+2^2$

$\left(\sqrt{5}\right)^2-2\sqrt{5}\cdot \:2+2^2$

$\left(\sqrt{5}\right)^2$

$\sqrt{a}=a^{\frac{1}{2}}$

$=\left(5^{\frac{1}{2}}\right)^2$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}$

$=5^{\frac{1}{2}\cdot \:2}$

$\frac{1}{2}\cdot \:2=1$

$=5$

$2\sqrt{5}\cdot \:2=4\sqrt{5}$

$2^2=4$

$=5-4\sqrt{5}+4$

$\mathrm{Add\:the\:numbers:}\:5+4=9$

$=9-4\sqrt{5}$

Answer 2

$\mathfrak{\red{\underline{\underline{Question}}}}$

Simplify:

${(\sqrt{5} - 2)}^{2}$

$\mathfrak{\red{\underline{\underline{Answer}}}}$

$\boxed{ 9 - 4\sqrt{5}}$

$\mathfrak{\red{\underline{\underline{Step\: by\: Step\: Solution}}}}$

${(\sqrt{5} - 2)}^{2}$

Here,

$a = \sqrt{5} \\ b = 2$

We know,

$\boxed{{(a - b)}^{2} = a^{2} + b^{2} - 2ab}$

${(\sqrt{5} + 2)}^{2}$

$= {(\sqrt{5})}^{2} + {(2)}^{2} - 2(\sqrt{5})(2)$

$= 5 + 4 - 4\sqrt{5}$

$= 9 - 4\sqrt{5}$

Therefore,$\bold{{(\sqrt{5} - 2)}^{2} = 9 - 4\sqrt{5}}$