Simplify and clasbify the
tesult as rational or irrational

Ask by Rose Frazier. in South Africa

Jan 23,2025

Question

Simplify and clasbify the tesult as rational or irrational $$ \sqrt{8} \sqrt[3]{3 \frac{y}{6}} $$

UpStudy AI · Accepted Answer

Calculate or simplify the expression $$ \sqrt{8} \sqrt[3]{3 \frac{y}{6}} $$.
Simplify the expression by following steps:
- step0: Solution:
  $$\sqrt{8}	imes \sqrt[3]{3	imes \frac{y}{6}}$$
- step1: Simplify the root:
  $$2\sqrt{2}	imes \sqrt[3]{3	imes \frac{y}{6}}$$
- step2: Multiply the terms:
  $$2\sqrt{2}	imes \sqrt[3]{\frac{y}{2}}$$
- step3: Use the properties of radicals:
  $$2\sqrt{2}	imes \frac{\sqrt[3]{y}}{\sqrt[3]{2}}$$
- step4: Multiply the terms:
  $$\frac{2\sqrt{2}	imes \sqrt[3]{y}}{\sqrt[3]{2}}$$
- step5: Multiply the terms:
  $$\frac{2\sqrt[6]{8y^{2}}}{\sqrt[3]{2}}$$
- step6: Simplify:
  $$2\sqrt[6]{2y^{2}}$$
The simplified form of $$ \sqrt{8} \sqrt[3]{3 \frac{y}{6}} $$ is $$ 2\sqrt[6]{2y^{2}} $$.

This result is a rational number because it can be expressed as a finite decimal or a fraction. Therefore, the result is rational.
The simplified form is $$ 2\sqrt[6]{2y^{2}} $$, which is a rational number.

Simplify and clasbify the
tesult as rational or irrational

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