simplify −3√10 (√15 − 2√10)
To simplify the expression, we can use the distributive property of multiplication over addition/subtraction.
−3√10 (√15 − 2√10) = −3√10 * √15 - 3√10 * 2√10
To multiply the square roots, we can combine the radicals using the product rule, which states that √a * √b = √(a*b).
= −3√(10 * 15) - 3√(10 * 2√10)
Simplifying further,
= −3√150 - 3√(20√10)
We can't simplify the square root of 150, so we leave it as is. For 20√10, we can simplify it by using the product rule again:
3√(20√10) = 3 * √(20 * 10) = 3 * √(200) = 3 * 10√2 = 30√2
Substituting this back into the expression:
= −3√150 - 30√2
Thus, the simplified expression is −3√150 - 30√2.
To simplify the expression −3√10 (√15 − 2√10), we can use the distributive property of multiplication over addition/subtraction.
First, distribute −3√10 to both terms inside the parentheses:
−3√10 × √15 = −3√(10 × 15) = −3√150
−3√10 × 2√10 = −6√(10 × 10) = −6√100
Simplifying further:
−3√150 can be simplified as −3√(25 × 6) = −3√25 × √6 = −3 × 5√6 = −15√6
−6√100 can be simplified as −6 × 10 = −60
Putting it all together:
−3√10 (√15 − 2√10) = −15√6 − 60
To simplify the expression −3√10 (√15 − 2√10), we can distribute the −3√10 to each term inside the parentheses.
First, let's distribute the −3√10 to √15:
−3√10 ∙ √15 = −3√(10∙15) = −3√150
Next, let's distribute the −3√10 to −2√10:
−3√10 ∙ −2√10 = 6√(10∙10) = 6√100
Now we have:
−3√10 (√15 − 2√10) = −3√150 + 6√100
To simplify further, let's evaluate the square roots of 150 and 100:
√150 = 5√6
√100 = 10
Substituting these values back into the expression:
−3√10 (√15 − 2√10) = −3√150 + 6√100 = −3(5√6) + 6(10) = −15√6 + 60
Therefore, the simplified expression is −15√6 + 60.