Ising a calculator, determine between which two integers the following numbers lie. Then verify your answers by using a calculator 50 $$ \begin{array}{llll}30 & ext { (2) } \sqrt{29} & ext { (3) } \sqrt[3]{45} & ext { (4) }-\sqrt{54} \ ext { (6) } \pi^{4} & \end{array} $$

Question

Ising a calculator, determine between which two integers the following numbers lie. Then verify your answers by using a calculator 50 $$ \begin{array}{llll}30 & 	ext { (2) } \sqrt{29} & 	ext { (3) } \sqrt[3]{45} & 	ext { (4) }-\sqrt{54} \ 	ext { (6) } \pi^{4} & \end{array} $$

UpStudy AI · Accepted Answer

To determine between which two integers the given numbers lie, we will evaluate each expression step by step.

1. **For $$30$$**:
   - This is already an integer. It lies between $$30$$ and $$30$$.

2. **For $$\sqrt{29}$$**:
   - We know that $$5^2 = 25$$ and $$6^2 = 36$$. Therefore, $$\sqrt{29}$$ lies between $$5$$ and $$6$$.

3. **For $$\sqrt[3]{45}$$**:
   - We know that $$3^3 = 27$$ and $$4^3 = 64$$. Therefore, $$\sqrt[3]{45}$$ lies between $$3$$ and $$4$$.

4. **For $$-\sqrt{54}$$**:
   - First, we find $$\sqrt{54}$$. We know that $$7^2 = 49$$ and $$8^2 = 64$$. Therefore, $$\sqrt{54}$$ lies between $$7$$ and $$8$$. Thus, $$-\sqrt{54}$$ lies between $$-8$$ and $$-7$$.

5. **For $$\pi^{4}$$**:
   - We know that $$\pi \approx 3.14$$. Therefore, $$\pi^4 \approx (3.14)^4$$. We can calculate this to find the exact range.

Now, let's calculate $$\pi^4$$ to find the integers it lies between.

I'll perform the calculations for $$\sqrt{29}$$, $$\sqrt[3]{45}$$, $$-\sqrt{54}$$, and $$\pi^4$$ to confirm the ranges.
Calculate the value by following steps:
- step0: Calculate:
  $$\pi ^{4}$$
Calculate or simplify the expression $$ \sqrt(29) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{29}$$
Calculate or simplify the expression $$ (45)^(1/3) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$45^{\frac{1}{3}}$$
- step1: Transform the expression:
  $$\sqrt[3]{45}$$
Calculate or simplify the expression $$ -\sqrt(54) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$-\sqrt{54}$$
- step1: Simplify the root:
  $$-3\sqrt{6}$$
Now that we have calculated the values, let's summarize the results:

1. **For $$30$$**:
   - Lies between $$30$$ and $$30$$.

2. **For $$\sqrt{29}$$**:
   - $$\sqrt{29} \approx 5.385$$
   - Lies between $$5$$ and $$6$$.

3. **For $$\sqrt[3]{45}$$**:
   - $$\sqrt[3]{45} \approx 3.557$$
   - Lies between $$3$$ and $$4$$.

4. **For $$-\sqrt{54}$$**:
   - $$-\sqrt{54} \approx -7.348$$
   - Lies between $$-8$$ and $$-7$$.

5. **For $$\pi^{4}$$**:
   - $$\pi^{4} \approx 97.409$$
   - Lies between $$97$$ and $$98$$.

### Summary of Results:
- $$30$$: between $$30$$ and $$30$$
- $$\sqrt{29}$$: between $$5$$ and $$6$$
- $$\sqrt[3]{45}$$: between $$3$$ and $$4$$
- $$-\sqrt{54}$$: between $$-8$$ and $$-7$$
- $$\pi^{4}$$: between $$97$$ and $$98$$

These results can be verified using a calculator, and they confirm the ranges we have determined.
- $$30$$ lies between $$30$$ and $$30$$. - $$\sqrt{29}$$ lies between $$5$$ and $$6$$. - $$\sqrt[3]{45}$$ lies between $$3$$ and $$4$$. - $$-\sqrt{54}$$ lies between $$-8$$ and $$-7$$. - $$\pi^{4}$$ lies between $$97$$ and $$98$$.

Ising a calculator, determine between which two integers the following
numbers lie. Then verify your answers by using a calculator
50

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