Multiply / Divide Radical Expressions.
Express in simplest radical form.
√5 √50
To multiply radical expressions, you can simply multiply the numbers outside the radical sign and multiply the numbers inside the radical sign separately.
The expression is: √5 * √50
Outside the radical sign: √5 * √50 = √(5*50) = √250
Inside the radical sign: √5 * √50 = √(5*50) = √250
Therefore, the expression √5 * √50 in simplest radical form is √250.
To multiply or divide radical expressions, you can simply multiply or divide the numbers inside the radicals and combine the radicals if possible.
In this case, we have √5 multiplied by √50.
Step 1: Multiply the numbers inside the radicals:
√5 * √50 = √(5 * 50) = √250
Step 2: Simplify the radical if possible:
To simplify √250, we can look for perfect square factors. The factors of 250 are 2 * 5 * 5 * 5. We can pair 2 of the 5's to get a perfect square:
√250 = √(2 * 5 * 5 * 5) = √(2 * 5^2 * 5) = √(2 * 5^3)
Step 3: Take out the perfect square from the radical:
√(2 * 5^3) = √(2) * √(5^2 * 5) = √(2) * 5√5
So, the expression √5 √50, in simplest radical form, is 5√5√2 or 5√10.
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To multiply radical expressions, you can multiply the numbers outside the radical sign and the numbers inside the radical sign separately.
The expression is √5 * √50.
Outside the radical sign: √5 * √50 = √(5 * 50) = √250.
Inside the radical sign: √5 * √50 = √(5 * 50) = √250.
Therefore, the expression √5 * √50 in simplest radical form is √250.
To simplify the radical expression √5 √50, you can follow these steps:
Step 1: Rewrite the radicals as the product of their factors.
√5 √50 = √(5 * 50)
Step 2: Simplify the multiplication inside the radical.
√(5 * 50) = √250
Step 3: Determine the largest perfect square that divides evenly into the radicand (250). In this case, it is 25.
√250 = √(25 * 10)
Step 4: Simplify the perfect square inside the radical.
√(25 * 10) = √25 * √10
Step 5: Simplify the remaining radical.
√25 = 5
Putting it all together:
√5 √50 = 5√10
Therefore, the expression √5 √50 simplified to its simplest radical form is 5√10.