Operations with Radicals

Mathematical Equivalence

ON

Answer explanation

The square roots of 13 are like terms. Add 1 and -5 together.

The other term is still separate.

Mathematical Equivalence

ON

Answer explanation

The square roots of 2 are like terms. Add 7 and -1 together.

The other term is still separate.

Mathematical Equivalence

OFF

Answer explanation

50 factors to 25 and 2.

The square root of 25 is 5.

2 stays under the radical.

98 factors to 49 and 2.

The square root of 49 is 7.

2 stays under the radical.

Adding 7 and 5 equals 12.

2 stays under the radical.

Mathematical Equivalence

OFF

Answer explanation

24 x 3 = 72.

72 factors to 36 and 2.

The square root of 36 is 6.

The 2 stays under the radical.

Mathematical Equivalence

ON

Answer explanation

8 x 18 = 144.

Square root of 144 is 12.

x * x^5 = x^6.

Square root of x^6 is x^3.

Final answer has no radical.

Mathematical Equivalence

OFF

Answer explanation

6 x 2 = 12

12 factors to 4 and 3

Square root of 4 is 2, 3 stays under the radical.

x^3* x^10 = x^13

x^13 factors to x^12 and x.

Square root of x^12 is x^6, x stays under the radical.

Mathematical Equivalence

ON

Answer explanation

3 x 12 = 36.

Square root of 36 is 6.

3 x 6 = 18.

18 factors to 9 and 2.

Square root of 9 is 3.

2 stays under the radical.

Tags

CCSS.HSN.RN.A.2

Mathematical Equivalence

OFF

Answer explanation

Distribute 5 to 10 and 40, and you get 50 and 200.

50 factors to 25 and 2. The square root of 25 is 5, 2 stays under the radical.

200 factors to 100 and 2. The square root of 100 is 10, 2 stays under the radical.

Multiply 7 x 5 and -4 x 10.

Combine the coefficient, keep 2 under the radical.

Tags

CCSS.HSN.RN.A.2

Mathematical Equivalence

OFF

Answer explanation

Distribute 2 to 6 and 24, and you get 12 and 48.

12 factors to 4 and 3. The square root of 4 is 2, 3 stays under the radical.

48 factors to 16 and 3. The square root of 16 is 4, 3 stays under the radical.

Multiply 3 x 2 and 5 x 4.

Combine the coefficients, keep 3 under the radical.

Tags

CCSS.HSN.RN.A.2

Mathematical Equivalence

OFF

Answer explanation

Distribute 2, then distribute square root 3.

The middle terms cancel out.

You have 4 minus 3, which equals 1.

Tags

CCSS.HSN.RN.A.2