5√8×3√4
To simplify the expression 5√8 × 3√4, we can combine the radicals under the same radical sign and then multiply the coefficients (outside the radical sign) together.
√8 can be simplified as √(4 × 2) = 2√2, since 4 is a perfect square factor.
√4 can be simplified as √(4) = 2, since 4 is a perfect square.
Now, we have 5(2√2) × 3(2).
Multiplying the coefficients: 5 × 3 × 2 = 30.
Multiplying the radicals: 2√2 × 2 = 4√2.
Therefore, 5√8 × 3√4 simplifies to 30√2.
To simplify the expression 5√8 × 3√4, we can multiply the numbers outside the square roots and multiply the numbers inside the square roots separately.
Let's break it down step by step:
Step 1:
The expression is 5√8 × 3√4.
Multiply the numbers outside the square roots: 5 × 3 = 15.
Step 2:
Inside the square roots, √8 can be simplified further.
√8 can be written as √(4 × 2).
Since the square root of 4 is 2, we can simplify to 2√2.
Step 3:
Inside the other square root, √4 simplifies to 2.
Now we have 15 × 2√2 × 2.
Step 4:
Multiply the numbers outside the square root: 15 × 2 × 2 = 60.
So, the simplified expression is 60√2.
To simplify the expression 5√8 × 3√4, we can start by simplifying each square root separately.
√8 can be further simplified as follows:
√8 = √(4 × 2)
= √4 × √2
= 2√2
√4 is already simplified as 2.
Now, let's substitute the simplified square roots back into the expression:
5√8 × 3√4 = 5(2√2) × 3(2)
Next, we can multiply the coefficients and simplify the expression:
5(2√2) × 3(2) = (5 × 2 × 3)√2
= 30√2
So, 5√8 × 3√4 simplifies to 30√2.