What is the length of the hypotenuse in this right triangle? a. 3cm b. 3 (square root) 2cm c. 5 (square root) 3cm d. 9 cm

B. 3 (square root) 2cm

Step-by-step explanation:

using pythagorean theorem

a^2 + b^2 =c^2  where a and b are the legs and c is the hypotenuse

3^2 + 3^2 = c^2

9+9 =c^2

18 = c^2

take the square root of each side

sqrt(18) = sqrt(c^2)

sqrt(9 *2) = c

sqrt(9) sqrt(2) = c

3 sqrt(2) =c

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.