Simplify the following expressions.
- Thread starter nikeamc44
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I'm sorry, but we'll need more information. You say that the expression is inside a radical, and that the radical is them cubed. But what is the index of the radical?nikeamc44 said:
When you reply, please show the steps you have tried so far (even if you think they are wrong).
Thank you.
Eliz.
Hello, nikeamc44!
I assume you meant: \(\displaystyle \;\) 125a^15 b^8 c^4 all under a cube root.
Use the same routine for simplifying square roots,
\(\displaystyle \;\;\)except we want factors which are perfect <u>cubes</u>.
\(\displaystyle \L\;\;\sqrt[3]{125\cdot a^{15}\cdot b^8\cdot c^4}\)
\(\displaystyle \L\;\;=\;\sqrt[3]{125(a^{15})(b^6\cdot b^2)(c^3\cdot c)}\)
\(\displaystyle \L\:\;\;=\;\sqrt[3]{(125a^{15} b^6 c^3)(b^2c)}\)
\(\displaystyle \L\;\;\;=\;\sqrt[3]{125a^{15}b^6c^3}\,\cdot\,\sqrt[3]{b^2c}\)
\(\displaystyle \L\;\;\;=\;5a^3b^2c\,\sqrt[3]{b^2c}\)
I assume you meant: \(\displaystyle \;\) 125a^15 b^8 c^4 all under a cube root.
Use the same routine for simplifying square roots,
\(\displaystyle \;\;\)except we want factors which are perfect <u>cubes</u>.
\(\displaystyle \L\;\;\sqrt[3]{125\cdot a^{15}\cdot b^8\cdot c^4}\)
\(\displaystyle \L\;\;=\;\sqrt[3]{125(a^{15})(b^6\cdot b^2)(c^3\cdot c)}\)
\(\displaystyle \L\:\;\;=\;\sqrt[3]{(125a^{15} b^6 c^3)(b^2c)}\)
\(\displaystyle \L\;\;\;=\;\sqrt[3]{125a^{15}b^6c^3}\,\cdot\,\sqrt[3]{b^2c}\)
\(\displaystyle \L\;\;\;=\;5a^3b^2c\,\sqrt[3]{b^2c}\)