Multiply / Divide Radical Expressions.
Express in simplest radical form.
√14 √35
√14 * √35 = √(14 * 35) = √(490) = √(49*10) = √(7^2 * 10) = √(7^2) * √10 = 7√10
To multiply or divide radical expressions, we can simply multiply or divide the numbers that are outside the radical (√).
In this case, we want to multiply √14 by √35.
√14 * √35 = √(14 * 35)
To simplify this further, we can find the prime factors of 14 and 35.
14 = 2 * 7
35 = 5 * 7
Now, let's find the shared factors between 14 and 35, which is 7.
So, we can rewrite 14 * 35 as (2 * 7) * (5 * 7) = 2 * 5 * 7 * 7
Now, let's take the square root of this expression.
√(2 * 5 * 7 * 7) = √(2 * 5) * √(7 * 7) = √10 * 7
Therefore, √14 * √35 simplifies to √10 * 7 in its simplest radical form.
To multiply or divide radical expressions, we can use the product and quotient rules of radicals.
To multiply radical expressions, we multiply the numbers under the radical sign (known as the radicand) and simplify if possible. In this case, we want to multiply √14 and √35.
√14 * √35 = √(14 * 35) = √490
To simplify √490, we need to find the largest perfect square that divides evenly into 490. The largest perfect square that divides 490 is 49 (7^2) since 49 * 10 = 490.
√490 = √(49 * 10) = √49 * √10 = 7√10
Therefore, the expression √14 * √35 simplifies to 7√10.
On the other hand, to divide radical expressions, we divide the numbers under the radical sign and simplify if possible. In this case, we have √14 ÷ √35.
√14 ÷ √35 = (√14 / √35)
To simplify √14 / √35, we need to rationalize the denominator. To do this, we multiply both the numerator and denominator by the conjugate of the denominator (√35).
(√14 / √35) * (√35 / √35) = (√14 * √35) / (√35 * √35) = (√(14 * 35)) / (√(35 * 35)) = √490 / 35
We can simplify this further by finding the largest perfect square that divides evenly into 490, which is 49 (7^2).
√490 / 35 = (√49 * √10) / 35 = 7√10 / 35 = (√10 / 5)
Therefore, the expression √14 ÷ √35 simplifies to (√10 / 5) in simplest radical form.