Question

I need a lot of help with practice problems, I am not understanding math right now. Please help!!!!!! Will give brainliest!!

Answer 1

Answer:

1.

The expression is $3^{3}\sqrt{21} -6^{3}\sqrt{2a}$

We need to solve each power: $27\sqrt{21}-216\sqrt{2a}$.

The Greatest common factor between 27 and 216 is 27, so we extract that

$27(\sqrt{21}- 8\sqrt{2a})$, which is the simplest form.

2.

The expression is $3^{\frac{1}{2} } \times 3^{\frac{1}{2} }$

Notice that bases are equal, that means we need to sum exponents only to find the simplest form

$3^{\frac{1}{2} +\frac{1}{2} }=3^{1}=3$

3.

The expression is $\sqrt[n]{x^{m} }$

Here we transform the root into a fractional exponent.

$\sqrt[n]{x^{m} }=x^{\frac{m}{n} }$

4.

The expression is

$\frac{\sqrt{250x^{16} } }{\sqrt{2x} }$

Here we need to express it as the root of a fraction

$\sqrt{\frac{250x^{16} }{2x} }$

Then, we divide

$\sqrt{\frac{250x^{16} }{2x} }=\sqrt{125x^{10-1} } =\sqrt{125x^{9} }$

5.

The equation is $\sqrt{2x+13}-5=x$

First, we move the term 5 to other side, then we elevate the equality to the square power to eliminate the square root. Consequently, we have to solve the square power of the binomial x+5:

$(\sqrt{2x+13} )^{2} =(x+5)^{2} \\2x+13=x^{2} +10x+25$

Then, we move all terms to one side

$x^{2} +10x+25-2x-13=0\\x^{2} +8x+12=0$

Now, we have to find to numbers which product is 12 and which sum is 8, those numbers are 6 and 2:

$\x^{2} +8x+12=(x+6)(x+2)$

The solutions are -6 and -2.

6.

The expression is

$3\sqrt[5]{(x+2)^{3} } +3=27$

First, we subtract the equation by 3, then we divide by 3:

$3\sqrt[5]{(x+2)^{3} } 3-3 =27-3\\3\sqrt[5]{(x+2)^{3} } =24\\\frac{3\sqrt[5]{(x+2)^{3} } }{3}=\frac{24}{3}\\ \sqrt[5]{(x+2)^{3} } =8$

Then, we elevate each side to the fifth power to eliminate the root

$(\sqrt[5]{(x+2)^{3} } )^{5} =8^{5} \\(x+2)^{3} =32768$

Now, we apply a cubic root to each side

$\sqrt[3]{(x+2)^{3}} =\sqrt[3]{32768} \\x+2=32\\x+2-2=32-2\\ \therefore x=30$

Answer 2

Answer:

1. 18 (sqrt21 - sqrt2a)

2. 3

3. x^m/n

4. (5x^4√10)/(√2x)

5. x = -2 or -6

6. x = 30

Step-by-step explanation:

Number 1

3^3sqrt21 - 6^3sqrt2a

3 * 6 * sqrt21 - sqrt2a

18 (sqrt21 - sqrt2a)

Number 2

3^1/2 * 3^1/2 =

3^1/2+1/2 =

3^1 =

3

Number 3

^nsqrtx^m =

x^m/n

Number 4

(√250x^16)/(√2x) =

(√25 * 10 * x^16)/√(2x )=

(5x^4√10)/(√2x)

Number 5

√2x + 13 - 5 = x

√2x + 13 = x + 5

square both side to take away the sqrt sign

(√2x + 13)^2 = (x + 5)^2

expand the equation on the RHS

2x + 13 = x(x+5) + 5(x+5)

2x+13 = x^2 + 10x +25

substract 13 from both sides

2x = x^s + 10x +12

subtract 2x from both sides

0 = x^2 +8x + 12

Factorize equation

x^2 + 6x +2x + 12 = 0

x(x+6) + 2(x+6) = 0

(x+2)(x+6) = 0

x = -2 or -6

Number 6

3 ^5sqrt(x+2)^3 + 3 = 27

subtract 3 from both sides

3 ^5sqrt(x+2)^3  = 27 - 3

3 ^5sqrt(x+2)^3  = 24

divide through by 3

^5sqrt(x+2)^3  = 8

square both sides by 5 to take away the 5th root sign

(x+2)^3  = (8)^5

(x+2)^3  = 32,768

take the cube root of both sides to take away the ^3

x+2 = ^3sqrt 32,768

x+2 = 32

x = 32 - 2

x = 30