To simplify the expression √3 × √21, we can use a property of square roots. This property states that the square root of a product is equal to the product of the square roots. So we can rewrite the expression as:
√3 × √21 = √(3 × 21).
Next, we need to multiply the numbers inside the square root:
3 × 21 = 63.
Therefore, we can simplify the expression to:
√63.
Now we look for perfect squares that divide 63. The number 63 can be factored into:
63 = 9 × 7,
and since 9 is a perfect square, we can simplify further:
√63 = √(9 × 7) = √9 × √7 = 3√7.
So, the simplified form of √3 × √21 is:
3√7.