Question

question
express in simplest radical form given ( x > 0 ).
( xsqrt{28x^2} - 4sqrt{63x^4} )

Explanation:

Step1: Simplify each radical term

First, simplify \(x\sqrt{28x^{2}}\). We can factor \(28\) as \(4\times7\), so \(\sqrt{28x^{2}}=\sqrt{4\times7\times x^{2}}\). Since \(x > 0\), \(\sqrt{x^{2}}=x\) and \(\sqrt{4} = 2\). Thus, \(x\sqrt{28x^{2}}=x\times2x\sqrt{7}=2x^{2}\sqrt{7}\).

Next, simplify \(4\sqrt{63x^{4}}\). Factor \(63\) as \(9\times7\), so \(\sqrt{63x^{4}}=\sqrt{9\times7\times x^{4}}\). \(\sqrt{9}=3\) and \(\sqrt{x^{4}}=x^{2}\) (since \(x>0\)). Thus, \(4\sqrt{63x^{4}} = 4\times3x^{2}\sqrt{7}=12x^{2}\sqrt{7}\).

Step2: Subtract the two simplified terms

Now, we have \(2x^{2}\sqrt{7}-12x^{2}\sqrt{7}\). Combining like terms (since both terms have \(x^{2}\sqrt{7}\)), we get \((2 - 12)x^{2}\sqrt{7}=- 10x^{2}\sqrt{7}\).

Answer:

\(-10x^{2}\sqrt{7}\)