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Question 1 of 4
Simplify
10√8+3√12−√27
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A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.
Evaluate the coefficients of like terms (same radicand).
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10√8+3√12−√27 |
Find two multiples of 8, 12 and 27 each where one is a perfect square. |
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10×√4×√2+3×√4×√3−√9×√3 |
Simplify |
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10×2√2+3×2√3−3√3 |
4 and 9 are perfect squares |
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20√2+6√3−3√3 |
|
= |
20√2+6−3√3 |
Evaluate coefficients |
|
= |
20√2+3√3 |
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Question 2 of 4
Simplify
6√18+√72−√75
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A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.
Evaluate the coefficients of like terms (same radicand).
|
= |
6√18+√72−√75 |
Find two multiples of 18, 72 and 75 each where one is a perfect square. |
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6×√9×√2+√36×√2−√25×√3 |
Simplify |
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6×3√2+6√2−5√3 |
9, 36 and 25 are perfect squares |
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18√2+6√2−5√3 |
|
= |
18+6√2−5√3 |
Evaluate coefficients |
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= |
24√2−5√3 |
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Question 3 of 4
Simplify
√18+√128−6√2
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A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.
Evaluate the coefficients of like terms (same radicand).
|
= |
√18+√128−6√2 |
Find two multiples of 18 and for 128 where one is a perfect square. |
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√9×√2+√64×√2−6√2 |
Simplify |
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3√2+8√2−6√2 |
9 and 64 are perfect squares. |
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= |
3√2+8√2−6√2 |
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= |
5√2 |
Evaluate coefficients |
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= |
5√2 |
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Question 4 of 4
Simplify
√600+√150−12√6
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A radicand is the number under the square root symbol.
Terms with the same radicand are like terms. We can evaluate the coefficients of like terms.
Evaluate the coefficients of like terms (same radicand).
|
= |
√600+√150−12√6 |
Find two multiples of 600 and for 150 each where one is a perfect square. |
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√100×√6+√25×√6−12√6 |
Simplify |
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= |
10√6+5√6−12√6 |
100 and 25 are perfect squares |
|
= |
10√6+5√6−12√6 |
|
= |
10+5−12√6 |
Evaluate coefficients |
|
= |
3√6 |
