Simplifying Radicals
BySimplify.
sqrt50
5sqrt2
Add.
5sqrt7+8sqrt7
13sqrt7
Subtract.
sqrt6-6sqrt6
-5sqrt6
Multiply. Write all answers as simplified radicals.
5sqrt2(4sqrt5)
20sqrt10
Use the Pythagorean theorem a2 + b2 = c2 to find the missing hypotenuse for the triangle with legs 3 and 4 cm long
5 cm
Simplify.
sqrt(96)
4sqrt6
Add.
3sqrt5+4sqrt3+sqrt5
4sqrt5+4sqrt3
Subtract.
7sqrt3-4sqrt3-2sqrt3
sqrt3
Multiply. Write all answers as simplified radicals.
-3sqrt3(6sqrt6)
-54sqrt2
Use the Pythagorean theorem a2 + b2 = c2 to find the missing hypotenuse for the triangle whose legs are 6 and 8.
10
Simplify.
-5sqrt27
-15sqrt3
Add.
5sqrt2+sqrt8
7sqrt2
Subtract.
sqrt(4)-sqrt25
-3
Multiply. Write all answers as simplified radicals.
(3sqrt5)^2
45
Use the Pythagorean theorem a2 + b2 = c2 to find the missing hypotenuse for the triangle whose legs are 5 and 12.
13
Simplify.
sqrt(72)
6sqrt2
Add.
sqrt98+sqrt32
11sqrt2
Subtract.
8sqrt8-sqrt200
6sqrt2
Multiply. Write all answers as simplified radicals.
(-3sqrt3)^2
27
Use the Pythagorean theorem a2 + b2 = c2 to find the missing hypotenuse for the triangle whose legs are 9 and 12.
15
Simplify.
sqrt450
15sqrt2
Add.
3sqrt75+4sqrt12
23sqrt3
sqrt125-sqrt45-sqrt98-4sqrt8
2sqrt5-15sqrt2
Multiply. Write all answers as simplified radicals.
3sqrt6(5sqrt3-sqrt2)
45sqrt2-6sqrt3
Use the Pythagorean theorem a2 + b2 = c2 to find the missing hypotenuse for the triangle whose legs are 12 and 16.
20