Answer :
The rationalize of all denominators is [tex]40x^{14} y^{20} i[/tex]
We rationalize the denominator to make certain that it will become less complicated to carry out any calculation at the rational number. while we rationalize the denominator in a fraction, then we are eliminating any radical expressions inclusive of rectangular roots and dice roots from the denominator.
The distinction is that denial flat out says there may be no trouble whilst clarification is smarter, it justifies thoughts and behaviors on some different grounds in the try to convince Self and others that these minds and behaviors are not maladaptive, that they may be definitely adaptive.
The rationalize is a disavowal defense mechanism that permits an individual to address emotional conflicts, or inner or external stressors, via devising reassuring or self-serving however incorrect factors for his or her personal or others' mind, actions, or feelings, which cowl up different reasons (Perry 1990).
[tex]5 \sqrt{-64 x^{14} y^{20} }[/tex]
[tex]\sqrt{-64} = i8[/tex]
[tex]5i8x^{14} y^{20}[/tex]
[tex]40ix^{14} y^{20}[/tex]
[tex]40x^{14} iy^{20}[/tex]
= [tex]40x^{14} y^{20} i[/tex]
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After simplifying the radical expression 5 √(-64) x¹⁴ y²⁰, the result is 40 x¹⁴ y²⁰ i.
We are given the radical expression as:
5 √(-64) x¹⁴ y²⁰
We need to simplify the radical expression and find the value of the expression.
Now, we will first simplify the term √(-64)
We know that:
√(-64) = √( - 1 × 8 × 8 )
= 8 √ -1
Using the properties of complex numbers, we get that:
√ - 1 = i
= 8 i
Putting it in the expression, we get that:
= 5 ( 8 i ) x¹⁴ y²⁰
= 40 x¹⁴ y²⁰ i
Therefore, we get that, after simplifying the radical expression 5 √(-64) x¹⁴ y²⁰, the result is 40 x¹⁴ y²⁰ i.
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