ros irracionales en la recta numérica. $$ \begin{array}{ll} ext { a. } \sqrt{81} & ext { d. } \sqrt{550} \ ext { b. } \sqrt{213} & ext { e. } \sqrt{1765} \ ext { c. } \sqrt{305} & ext { f. } \sqrt{7649} \ ext { g. } \sqrt{68646} & ext { h. } \sqrt{75876}\end{array} $$

Question

ros irracionales en la recta numérica. $$ \begin{array}{ll}	ext { a. } \sqrt{81} & 	ext { d. } \sqrt{550} \ 	ext { b. } \sqrt{213} & 	ext { e. } \sqrt{1765} \ 	ext { c. } \sqrt{305} & 	ext { f. } \sqrt{7649} \ 	ext { g. } \sqrt{68646} & 	ext { h. } \sqrt{75876}\end{array} $$

UpStudy AI · Accepted Answer

Para identificar los números irracionales en la recta numérica, primero calcularemos las raíces cuadradas de cada uno de los números dados. Luego, determinaremos si son irracionales o no.

Vamos a calcular cada raíz cuadrada:

1. $$ \sqrt{81} $$
2. $$ \sqrt{213} $$
3. $$ \sqrt{305} $$
4. $$ \sqrt{550} $$
5. $$ \sqrt{1765} $$
6. $$ \sqrt{7649} $$
7. $$ \sqrt{68646} $$
8. $$ \sqrt{75876} $$

Procederé a calcular estas raíces cuadradas.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{75876}{1}$$
- step1: Divide the terms:
  $$75876$$
Calculate or simplify the expression $$ \frac{550}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{550}{1}$$
- step1: Divide the terms:
  $$550$$
Calculate or simplify the expression $$ \frac{7649}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{7649}{1}$$
- step1: Divide the terms:
  $$7649$$
Calculate or simplify the expression $$ \frac{213}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{213}{1}$$
- step1: Divide the terms:
  $$213$$
Calculate or simplify the expression $$ \frac{81}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{81}{1}$$
- step1: Divide the terms:
  $$81$$
Calculate or simplify the expression $$ \frac{305}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{305}{1}$$
- step1: Divide the terms:
  $$305$$
Calculate or simplify the expression $$ \frac{68646}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{68646}{1}$$
- step1: Divide the terms:
  $$68646$$
Calculate or simplify the expression $$ \frac{1765}{1} $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1765}{1}$$
- step1: Divide the terms:
  $$1765$$
Ahora que hemos calculado las raíces cuadradas, podemos determinar cuáles son irracionales:

1. $$ \sqrt{81} = 9 $$ (racional)
2. $$ \sqrt{213} $$ (irracional)
3. $$ \sqrt{305} $$ (irracional)
4. $$ \sqrt{550} $$ (irracional)
5. $$ \sqrt{1765} $$ (irracional)
6. $$ \sqrt{7649} $$ (irracional)
7. $$ \sqrt{68646} $$ (irracional)
8. $$ \sqrt{75876} $$ (irracional)

**Conclusión:**
Los números irracionales en la recta numérica son:
- $$ \sqrt{213} $$
- $$ \sqrt{305} $$
- $$ \sqrt{550} $$
- $$ \sqrt{1765} $$
- $$ \sqrt{7649} $$
- $$ \sqrt{68646} $$
- $$ \sqrt{75876} $$

El único número racional es $$ \sqrt{81} $$.
Los números irracionales en la recta numérica son: $$ \sqrt{213} $$, $$ \sqrt{305} $$, $$ \sqrt{550} $$, $$ \sqrt{1765} $$, $$ \sqrt{7649} $$, $$ \sqrt{68646} $$ y $$ \sqrt{75876} $$.

ros irracionales en la recta numérica.

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