What is the simplified form of the expression? 2sqrt18 - 5sqrt32
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Answer

26√2

Step-by-step explanation:

The trick here lies in recognizing that both 18 and 32 have factors that are perfect squares:  18 = 2*9 and 32 = 2*16.  Therefore, we can write

2sqrt18 as 2√2√9, or 6√2, and 5sqrt32 as 5√2√16, or 20√2.

Then the original expression, in simplest form, is 6√2 + 20√2, or 26√2

5 sqrt 2

Step-by-step explanation:

Using the rule of radicals

sqrt a ×  sqrt b ⇔ sqrt ab

Simplify each radical

5 sqrt 8

= 5 sqrt 4(2)

= 5 × sqrt 4 × sqrt 2

= 5 × 2 × sqrt 2  = 10 sqrt 2

sqrt 18

= sqrt 9(2)

=  sqrt 9 × sqrt 2  = 3 sqrt 2

Putting it all together

10 sqrt 2 - 3 sqrt 2 - 2 sqrt 2

Collect like terms

=  sqrt 2 (10 - 3 - 2 ) = 5 sqrt 2

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2