Please help me simplify these radicals.

1)

http://img809.imageshack.us/img809/4886/radical.jpg

2)

http://img560.imageshack.us/img560/8733/radicaaaal.png

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- Aug 29th 2011, 06:17 AMgrandepuntoSimplifying Radicals
Please help me simplify these radicals.

1)

http://img809.imageshack.us/img809/4886/radical.jpg

2)

http://img560.imageshack.us/img560/8733/radicaaaal.png - Aug 29th 2011, 06:25 AMSironRe: Simplifying Radicals
What have you tried?

1)

Use basic rules like: $\displaystyle \sqrt[n]{x^{a}}=x^{\frac{a}{n}}$ and $\displaystyle a^{x}\cdot a^{y}=a^{x+y}$

2)

The same over here, you have to know some basic rules like: $\displaystyle (a-b)\cdot (a+b)=a^2-b^2$ and $\displaystyle (a+b)^2=a^2+2ab+b^2$

Try to use them where necessary and simplify. - Aug 29th 2011, 06:33 AMgrandepuntoRe: Simplifying Radicals
thank you. i will give it another try.

- Aug 29th 2011, 06:40 AMSironRe: Simplifying Radicals
Ok! You can show your work afterwards if you want :).

- Aug 29th 2011, 06:54 AMgrandepuntoRe: Simplifying Radicals
thanks for the help I did not put the "a" in a common root during the multiplication that was the error : )

- Aug 29th 2011, 07:08 AMSironRe: Simplifying Radicals
I have simplified it this way:

1)

$\displaystyle \sqrt[4]{a^{3}}+\sqrt[4]{a}\cdot \sqrt{a}+\frac{3\sqrt[4]{a^{9}}}{\sqrt{a^{3}}}$

$\displaystyle =a^{\frac{3}{4}}+a^{\frac{1}{4}}\cdot a^{\frac{1}{2}}+\frac{3a^{\frac{9}{4}}}{a^{\frac{3 }{2}}}$

$\displaystyle =a^{\frac{3}{4}}+a^{\frac{3}{4}}+3a^{\frac{3}{4}}= 5a^{\frac{3}{4}}}=5\sqrt[3]{a^{4}}$

2)

$\displaystyle (2\sqrt{7}-3)\cdot (2\sqrt{7}+3)-(\sqrt{7}+1)^2-(\sqrt{7}-2)^2$

$\displaystyle [(2\sqrt{7})^2-9]-(7+2\sqrt{7}+1}-(7-4\sqrt{7}+4)=28-9-7-2\sqrt{7}-1-7+4\sqrt{7}-4=2\sqrt{7}$