Question

) Diga o valor de cada x.
a) √49=x , pois7
2=49 x =
b) √
3
216=x, pois x
3=216 x =
c) √400=x, pois x
2=400
d) √
3
8000=x , pois x
3=x
X=
X

Answer 1

O valor de X, é:

• Item A: X= 7
• Item B: X= 6
• Item C: X = 20
• Item D: X= 20

Acompanhe a solução:

A radiciação é a operação inversa da potenciação. Desta forma, podemos entender que o índice da raiz, quando igual ao expoente do radicando fatorado, se anulam, restando como resultado da raiz a base do radicando fatorado.

Para fatorar, basta aplicar o Mínimo Múltiplo Comum (MMC).

Cálculos:

>>> Item A:

$\Large\begin {array}{l}\sqrt{49}=X\end {array}\\\\\\\Large\begin{array}{r | r}49&7\\7&7\\1\end{array}\\\\\\\\\Large\begin{array}{l}MMC(49)=7\cdot7=\boxed{\boxed{7^2}}\end{array}\\\\\\\\\\\\\therefore\LARGE\begin {array}{l}\sqrt[2]{49}=\underbrace{\sqrt[\not2]{7^\not^2}}_{\'indice\;e\;expoente=2}}=\Large\boxed{\boxed{7}}\Huge\checkmark\end {array}$

Assim, X= 7.

>>> Item B:

$\Large\begin {array}{l}\sqrt[3]{216}=X\end {array}\\\\\\\Large\begin{array}{r | r}216&2\\108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}\\\\\\\\\Large\begin{array}{l}MMC(216)=2\cdot2\cdot2\cdot3\cdot3\cdot3=\boxed{\boxed{2^3\cdot3^3}}\end{array}\\\\\\\\\\\\\therefore\LARGE\begin {array}{l}\sqrt[3]{216}=\underbrace{\sqrt[\not3]{2^\not^3\cdot3^\not^3}}_{\'indice\;e\;expoente=3}}=2\cdot3=\Large\boxed{\boxed{6}}\Huge\checkmark\end {array}$

Assim, X= 6.

>>> Item C:

$\Large\begin {array}{l}\sqrt[2]{400}=X\end {array}\\\\\\\Large\begin{array}{r | r}400&2\\200&2\\100&2\\50&2\\25&5\\5&5\\1\end{array}\\\\\\\\\Large\begin{array}{l}MMC(400)=2\cdot2\cdot2\cdot2\cdot5\cdot5=\boxed{\boxed{2^2\cdot2^2\cdot5^2}}\end{array}\\\\\\\\\\\\\therefore\LARGE\begin {array}{l}\sqrt[2]{400}=\underbrace{\sqrt[\not2]{2^\not^2\cdot2^\not^2\cdot5^\not^2}}_{\'indice\;e\;expoente=2}}=2\cdot2\cdot5=\Large\boxed{\boxed{20}}\Huge\checkmark\end {array}$

Assim, X= 20.

>>> Item D:

$\Large\begin {array}{l}\sqrt[3]{8000}=X\end {array}\\\\\\\Large\begin{array}{r | r}8000&2\\4000&2\\2000&2\\1000&2\\500&2\\250&2\\125&5&25&5\\5&5\\1\end{array}\\\\\\\\\Large\begin{array}{l}MMC(400)=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot5\cdot5\cdot5=\boxed{\boxed{2^3\cdot2^3\cdot5^3}}\end{array}\\\\\\\\\\\\\therefore\LARGE\begin {array}{l}\sqrt[3]{8000}=\underbrace{\sqrt[\not3]{2^\not^3\cdot2^\not^3\cdot5^\not^3}}_{\'indice\;e\;expoente=3}}=2\cdot2\cdot5=\Large\boxed{\boxed{20}}\Huge\checkmark\end {array}$

Assim, X= 20.

Resposta:

Portanto, o valor de X, é:

• Item A: X= 7
• Item B: X= 6
• Item C: X = 20
• Item D: X= 20

Se quiser saber mais, acesse:

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Bons estudos!