Operations with Radicals

Authored by Elizabeth Todd

Mathematics

9th Grade

CCSS covered

Used 15+ times

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MATH RESPONSE QUESTION

2 mins • 1 pt

Mathematical Equivalence

Answer explanation

The square roots of 13 are like terms. Add 1 and -5 together.
The other term is still separate.

MATH RESPONSE QUESTION

2 mins • 1 pt

Mathematical Equivalence

Answer explanation

The square roots of 2 are like terms. Add 7 and -1 together.
The other term is still separate.

MATH RESPONSE QUESTION

2 mins • 1 pt

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.

MATH RESPONSE QUESTION

2 mins • 1 pt

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.

MATH RESPONSE QUESTION

2 mins • 1 pt

Mathematical Equivalence

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.

MATH RESPONSE QUESTION

2 mins • 1 pt

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.

MATH RESPONSE QUESTION

2 mins • 1 pt

Mathematical Equivalence

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.

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Operations with Radicals

The square roots of 13 are like terms. Add 1 and -5 together.
The other term is still separate.

The square roots of 2 are like terms. Add 7 and -1 together.
The other term is still separate.

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.

24 x 3 = 72.
72 factors to 36 and 2.
The square root of 36 is 6.
The 2 stays under the radical.

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.

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.

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.

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.

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.

Distribute 2, then distribute square root 3.
The middle terms cancel out.
You have 4 minus 3, which equals 1.

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Operations with Radicals

The square roots of 13 are like terms. Add 1 and -5 together. The other term is still separate.

The square roots of 2 are like terms. Add 7 and -1 together. The other term is still separate.

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.

24 x 3 = 72.72 factors to 36 and 2.The square root of 36 is 6.The 2 stays under the radical.

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.

6 x 2 = 1212 factors to 4 and 3Square root of 4 is 2, 3 stays under the radical.x^3* x^10 = x^13x^13 factors to x^12 and x.Square root of x^12 is x^6, x stays under the radical.

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.

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.

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.

Distribute 2, then distribute square root 3.The middle terms cancel out.You have 4 minus 3, which equals 1.

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The square roots of 13 are like terms. Add 1 and -5 together.
The other term is still separate.

The square roots of 2 are like terms. Add 7 and -1 together.
The other term is still separate.

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.

24 x 3 = 72.
72 factors to 36 and 2.
The square root of 36 is 6.
The 2 stays under the radical.

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.

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.

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.

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.

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.

Distribute 2, then distribute square root 3.
The middle terms cancel out.
You have 4 minus 3, which equals 1.