MaxWong

1.\(\sqrt[6]{64}=2\)

2.\(\sqrt[3]{128}=2^{\frac{7}{3}}\)

3.\(\sqrt[10]{1024}=2\)

4. Wow here comes the hardest question

\(\sqrt[7]{\frac{-8\sqrt2}{2187}}=\frac{((-2)^\frac{3}{7})(2^\frac{1}{14})}{3}=-\frac{\sqrt2}{3}\)

Solve by substitution:

By considering the 3rd equation,

z=1+x

By considering the 2nd equation,

y=x+z=x+1+x=2x+1

Substitute these into the 1st equation,

x+(2x+1)+(1+x)=10

4x+2=10

2x+1=5

x=2

y = 2(2)+1 = 5

z = 1+(2) = 3

I love substitution method more, it's faster.

I assume you mean x^2-x=0

\(x^2-x=0\)Divide by x

\(x-1=0\)

\(x = 1\)

\(-8\sqrt{\frac{2}{2187}}\)

=\(\frac{-8\sqrt2}{27\sqrt3}\)

=\(-\frac{2^32^{\frac{1}{2}}}{3^33^{\frac{1}{2}}}\)

=\(-\frac{2^{\frac{7}{2}}}{3^{\frac{7}{2}}}\)

\(-(\frac{2}{3})^{\frac{7}{2}}\)

-2x=2

\(x=\frac{2}{-2}=-1\)

\(\sqrt{31+12\sqrt3}\)

=\(\sqrt{2^2+12\sqrt3+(3\sqrt3)^2}\)

=\(\sqrt{(2+3\sqrt3)^2}\)

=\(2+3\sqrt3\)

Hey! That is not a mathematical question!

Type '√' in your calculator and type that number, press '=' or 'EXE' and if you get a whole number, that number is a perfect square.

\(\frac{100%}{10%}=10\)