3sqrt(23) * 7sqrt(10) * sqrt(45)
3√23 * 7√10 * √45
3√23 * 7√10 * 3√5
(3*7*3)√(23*2*5*5)
(63)(5√46)
315√46
To simplify the expression 3√(23) * 7√(10) * √(45), we can first simplify each square root term individually and then multiply the resulting terms.
Step 1: Simplify square root terms:
- √(23) cannot be simplified further because 23 is not a perfect square.
- √(10) also cannot be simplified further because 10 is not a perfect square.
- √(45) can be simplified. We can factorize it as √(9 * 5), and since 9 is a perfect square, we can take it out of the square root, resulting in 3√(5).
Step 2: Combine the square root terms:
Now that we have simplified each square root term, we can multiply them together:
3√(23) * 7√(10) * √(45) = 3 * 7 * √(23) * √(10) * √(45)
Step 3: Simplify the coefficient:
Multiply the coefficients of the expression: 3 * 7 = 21.
Step 4: Multiply the square root terms:
Multiply the square root terms: √(23) * √(10) * √(45) = √(23 * 10 * 45) = √(10350)
So, the simplified expression is 21√(10350).