Consider the following example:<\/p>\n
Simplify 3√(6)*4√(7)<\/p>\n
Multiplying with radicals goes “number times number, radical times radical.” Like so:<\/p>\n
Step 1: Number times number: In our case, 3 times 4, which gives 12.<\/p>\n
Step 2: Radical times radical. In our case, √(6)√(7) gives √(42).<\/p>\n
Putting it all together, we get<\/p>\n
3√(6)*4√(7)=12√(42)<\/p>\n
So far, so good. Beware, though: a simplification can creep in when the radicals are multiplied together:<\/p>\n
Example 2: Simplify 3√(10)*7√(6)<\/p>\n
Solution: Using number times number, radical times radical, we get <\/p>\n
21√(60)<\/p>\n
From my earlier post on simplifying radicals,<\/a> we know we can’t just leave the answer 21√(60). After all, 60 contains the perfect square 4; we must simplify it as follows:<\/p>\n 21√(60)=21√(4)√(15)=21*2√(15)=42√(15)<\/p>\n Note that if one of the factors is missing the number part, you just imagine it’s a 1 and proceed:<\/p>\n 4√(7)*√(11)=4√(7)*1√(11)=4√(77)<\/p>\n On the other hand, one of the factors might be missing the radical part. Then, you just multiply the numbers together and tack the radical at the end:<\/p>\n 6√(5)*(8)=48√(5)<\/p>\n Visit again for more tips on operations with radicals:)<\/p>\n