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Answer :
To solve the expression [tex]\sqrt{16x^4 + 9x^4}[/tex], let's work step by step to simplify it.
Combine the like terms inside the square root:
The terms inside the square root are [tex]16x^4[/tex] and [tex]9x^4[/tex]. Since these are like terms (both are coefficients of [tex]x^4[/tex]), we can add them together:
[tex]16x^4 + 9x^4 = (16 + 9)x^4 = 25x^4[/tex]
Simplify the square root:
Now, we take the square root of [tex]25x^4[/tex]:
[tex]\sqrt{25x^4} = \sqrt{25} \cdot \sqrt{x^4}[/tex]
- [tex]\sqrt{25} = 5[/tex] since 25 is a perfect square.
- [tex]\sqrt{x^4} = x^2[/tex], because [tex]x^4[/tex] is [tex](x^2)^2[/tex], and the square root of [tex](x^2)^2[/tex] is [tex]x^2[/tex].
Thus, we have:
[tex]\sqrt{25x^4} = 5x^2[/tex]
This means the simplified form of [tex]\sqrt{16x^4 + 9x^4}[/tex] is [tex]5x^2[/tex]. When squaring and then taking the square root, always assume [tex]x[/tex] is a non-negative real number, or specify the domain if needed.
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